Geometry Lessons | Free Lessons, Practice Problems & Assessment

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Geometry: 01-Parallel and Perpendicular Lines

G002- Properties of Parallel lines

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G003- Proving Lines Parallel

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G005-Triangle Angle Sum and Exterior Angle Theorem

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G007-Equations of Lines in the Coordinate Plane

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G008-Writing Equations of Parallel and Perpendicular Lines

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Geometry: 02-Congruent Triangles

G009- Congruent Triangles

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G010-Triangle Congruence by SSS and SAS

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G011 - Triangle Congruence by ASA and AAS

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G012-Using Corresponding Parts of Congruent Triangles

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G013-Isosceles and Equilateral Triangles

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G014-Triangle Congruence by HL (Right Triangles)

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G015- Congruence in Overlapping Triangles

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Geometry: 03-Relationships with Triangles

G016-Midsegments of Triangles

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G018- Bisectors in Triangles

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G019- Medians & Altitudes

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G020- Indirect Proofs

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G021-Inequalities in a Triangle

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G022 - Inequalities in Two Triangles

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Geometry: 04-Polygons and Triangles

G023-Angle Sum Theorem for Convex Polygons

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G024-Properties of Parallelograms

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G025- Proving that a Quadrilateral is a Parallelogram

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G026- Properties of Rhombuses, Rectangles, and Squares

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G027- Conditions of Rhombuses, Rectangles, and Squares

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G028- Trapezoids and Kites

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G029- Polygons in the Coordinate Plane

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G030- Applying Coordinate Geometry

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G031- Proofs Using Coordinate Geometry

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G032-Solving Proportions

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G033-Similar Polygons and Proportions

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G034- Proving Triangles Similar

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G035- Similar Right Triangles

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G036- Proportions in Triangles

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Geometry: 06-Right Triangles and Trigonometry

G037 - Pythagorean Theorem

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G038-Special Right Triangles

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G039-Trigonometry

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G040- Elevation/Depression

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G041-Law of Sines

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G042-Law of Cosines

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Geometry: 07-Transformations

G043-Translations

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G044-Reflections

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G045-Rotations

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G046- Compositions of Isometries

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G047- Congruent Triangles and Congruence Transformations

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G048- Dilations

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G049- Similarity Transformation

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Geometry: 08-Area

G050- Area of Triangles and Parallelograms

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G051- Areas of Trapezoids, Rhombuses, and Kites

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G052-Area of Regular Polygons

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G053- Perimeter and Areas of Similar Figures

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G054-Trigonometry and the Area of Regular Polygons

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G055-Arc Measures and Arc Lengths in Circles

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G056-Sector Area and Area of a Segment

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G057- Geometric Probability

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Geometry: 09-Surface Area and Volume

G058- Space Figures and Cross Sections

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G059- Surface Areas of Prisms and Cylinders

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G060- Surface Areas of Pyramids and Cones

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G061-Volumes of Prisms and Cylinders

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G062-Volumes of Pyramids and Cones

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G063- Surface Area and Volumes of Spheres

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G064- Areas and Volumes of Similar Solids

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Geometry: 10-Circles

G065- Tangent Lines

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G066- Congruent Chords

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G067-Intersecting Chords (Segment Lengths)

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G068-Secants & Tangents w/ Vertex Outside of Circle (Segment Lengths)

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G069-Central Angles, Inscribed Angles and Arcs

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G070-Intersecting Chords (Arc and Angle Measures)

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G071-Tangent & Secant Lines w/ Vertex Outside of Circle (Arcs & Angles)

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G072-Chords Perpendicular to a Radius (Segment Measures)

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G073-Equation of a Circle

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I. Parallel and Perpendicular Lines

Lesson: Properties of Parallel Lines

Example: Identify each pair of angles as corresponding, alternate interior, alternate exterior, same-side interior, vertical, or adjacent.

Practice 01

Lesson: Proving Lines Parallel

Example: Find the measure of the indicated angle that makes the two lines parallel.

Practice 01

Lesson: Triangle Angle Sum and Exterior Angle Theorem

Example:Find the measure of each angle indicated.

Practice 01

Lesson: Equations of Lines in the Coordinate Plane

Example: Sketch the graph of the line $y=4x-9$

Practice 01

Lesson: Writing Equations of Parallel and Perpendicular Lines

Example: Write the slope-intercept form of the equation of a line that passed through (3, 4) and is parallel to $y=\dfrac{1}{3}x-5$ .

Practice 01

II. Congruent Triangles

Lesson: Congruent Triangles

Example: State if the two triangles are congruent. If they are, state how you know.

Practice 01

Lesson: Triangle Congruence by SSS and SAS

Example: State is the two triangles below are congruent, and if so state how you know.

Practice 01

Lesson: Triangle Congruence by ASA and AAS

Example: State is the two triangles below are congruent, and if so how?

Practice 01

Lesson: Identifying Corresponding Parts of Congruent Triangles

Example: Give that triangle ABC is congruent to triangle DEF, which pair of angles are congruent?

Practice 01

Lesson: Isosceles and Equilateral Triangles

Example: In $\triangle{XYZ}$ , $\angle{X} \cong \angle{Y}$
Which of the following statements is true?

Example: In $\triangle{XYZ}$ , $\angle{X} \cong \angle{Y}$ . If the measure of $\angle{X}$ is 50 degrees, and the measure of $\angle{Z}$ is $2x-8$ degrees, what is the value of $x$ ?

Practice 01

Lesson: Triangle Congruence by HL (Right Triangles)

Example: State is the two triangles below are congruent, and if so how?

Practice 01

Lesson: Congruence in Overlapping Triangles

Example: Given: $\overline{AB} \cong \overline{AC}$ , what postulate will prove $\triangle BAE \cong \triangle CAD$ ?

Practice 01

III. Relationships with Triangles

Midsegments of Triangles

Example: Find the length of VU

Practice 01

Angle Bisectors in Triangles

Example: Find the missing length indicated.

Practice 01

Bisectors in Triangles

Example: Find the measure of the indicated length.

Practice 01

Medians and Altitudes

Example: What is the measure of $\overline{BD}$ ?

Practice 01

Indirect Proofs

Example:What is the first step to this indirect proof?
$\angle A$ is acute

Practice 01

Lesson: Inequalities in a Triangle

Example:Order the sides of each triangle from shortest to longest.

Practice 01

Inequalities in Two Triangles

Example:
What theorem can be used to prove $\overline{AC} > \overline{DF}$ ?

Practice 01

IV. Polygons and Triangles

Lesson: Angle Sum Theorem for Convex Polygons

Example: What is the interior angle sum of a regular hexagon?

Practice 01

Lesson: Properties of Parallelograms

Example: Find the measurement indicated in the parallelogram.

Practice 01

Proving that a Quadrilateral is a Parallelogram

Example: Given that ABCD is a parallelogram, what is the value of $x$ ?

Practice 01

Properties of Rhombuses, Rectangles, and Squares

Lesson: Rhombuses

Lesson: Rectangles

Lesson: Squares

Example: Which figure below is a rhombus?

Practice 01

Conditions of Rhombuses, Rectangles, and Squares

Example: What value of $x$ in the figure below would make the figure a rectangle?

Practice 01

Trapezoids and Kites

Practice 01

Polygons in the Coordinate Plane

Example: Triangle ABC has vertices at points (2, 4), (5, 7) and (3, 6). Determine what type of triangle $\bigtriangleup$ ABC is.

Practice 01

Applying Coordinate Geometry

Example: Is a quadrilateral with vertices (-A, 0), (0, A), (A,0) and (0, -A) a square?

Practice 01

Proofs Using Coordinate Geometry

Example: Which theorem can be used to proved $\bigtriangleup ACD \cong \bigtriangleup CAB$ ?

Practice 01

Solving Proportions

Example: Solve for $x$
$\dfrac{5}{8}=\dfrac{x}{12}$

Practice 01

Similar Polygons and Proportions

Example: Solve for $x$

Practice 01

Proving Triangles Similar

Example:Given $\overline{BC} \parallel \overline{DE}$ , which theorem can be used to prove $\triangle ABC \sim \triangle ADE$

Practice 01

Similar Right Triangles

Example: Solve for $x$

Practice 01

Proportions in Triangles

Example:Find the missing length indicated

Practice 01

VI. Right Triangles and Trigonometry

Lesson: Pythagorean Theorem

Example: The hypotenuse of a right triangle has a length of 26 inches. One of its legs is 24 inches. What is the length of the other leg?

Practice 01

Special Right Triangles

Lesson: 30-60-90

Lesson: 45-45-90

Lesson: Pythagorean Triples

Example: A right triangle with an angle of measure 45 degrees, has a hypotenuse of length 13. What are the lengths of the other legs?

Practice 01

Lesson: Trigonometry

Example: Right triangle $\triangle ABC$ has the following side lengths: $\overline{AB}$ is 8 ft, $\overline{AC}$ is 3 ft. What is tan(A)?

Practice 01

Elevation and Depression

Example: The height of the Empire State Building is 1,050 feet. At the bottom, there is a basketball 450 feet away. Find the angle of depression from the top of the tower to the basketball.

Practice 01

Law of Sines

Example: In $\triangle ABC$ , the length of $\overline{AC}$ is 12 yd, the length of $\overline{AB}$ is 24 yd, and the measure of angle A is 30 degrees. What is the measure of angle B?

Practice 01

Law of Cosines

Example: In $\triangle ABC$ , the length of $\overline{AC}$ is 11.3 yd, the length of $\overline{BC}$ is 19.9 yd, and the measure of angle C is 112.4 degrees. What is the length of $\overline{AB}$ ?

Practice 01

VII. Transformations

Lesson: Translations

Example: $\triangle AHF$ has coordinates A (3, -1), H (5, -1), and F (1,-3). If $\triangle AHF$ is translated 1 unit left and 6 units up, what are the coordinates of its image $\triangle A'H'F'$ ?

Practice 01

Reflections

Lesson: Reflection Over an Axis

Lesson: Reflection Over a Horizontal or Vertical Line

Lesson: Reflection Over the Line y=x

Example: $\triangle ABC$ has coordinates A (2, 4), B (3, 6) and C (-2, -1). If $\triangle ABC$ is reflected across the x-axis, what are the coordinates of its image $\triangle A'B'C'$ ?

Practice 01

Lesson: Rotations

Example: $\triangle DEF$ has coordinates D (1, 1), E (3, 1) and F (2, 5). If the triangle is rotated 90 degrees about the origin, what are the coordintates of $\triangle D'E'F'$ ?

Practice 01

Compositions of Isometries

Example: What are the coordinates of the point $P(5,-2)$ after $(R_{origin} \circ T_{3,-2}) (P)$ ?

Practice 01

Congruent Triangles and Congruence Transformations

Example:

Practice 01

Lesson: Dilations

Example: Triangle $X(1,1)$ , $Y(3,2)$ , $Z(4,1)$ becomes triangle $X'(3,3)$ , $Y'(9,6)$ , $Z'(12,3)$ under a dilation. What would the scale factor be for this dilation?

Practice 01

Similarity Transformation

Example: When equilateral triangle $\triangle ABC$ is dilated by a factor of $\dfrac{1}{2}$ , what are the corresponding angle measurements of the image triangle?

Practice 01

VIII. Area

Area of Triangles and Parallelograms

Example: What is the area of a parallelogram with a base of 24 ft and a height of 20 ft?

Practice 01

Area of Trapezoids, Rhombuses, and Kites

Example: What is the area of a trapezoid with bases of 3 ft and 6 ft, with a height of 2.2 ft?

Practice 01

Area of Regular Polygons

Example: What is the area of a regular hexagon that has a side of length 14 inches and an apothem of 12.1 inches?

Practice 01

Perimeter and Area of Similar Figures

Example: The ratio of the perimeters of rectangle I to rectangle II is 1:3. If the area of rectangle I is 12 sq. ft., what is the are of rectangle II?

Practice 01

Trigonometry and the Area of Regular Polygons

Example: What is the area of an equilateral triangle with a side length of 6 m?

Practice 01

Arc Measures and Arc Lengths in Circles

Example: Find the measure of arc JK

Practice 01

Sector Area

Example: Find the area of each sector.

Practice 01

Geometric Probability

Example:A circle is inscribed in a square with the following measurements. What is the probability that a random point will lie in the circle? Leave your answers in terms of $\pi$ if necessary.

Practice 01

IX. Surface Area and Volume

Space Figures and Cross Sections

Example: Use Euler’s fourmula to determine the number of faces of a solid with 9 edges and 5 vertices.

Practice 01

Lesson: Surface Areas of Prisms and Cylinders

Example: Sketch the net of the solid below

Practice 01

Lesson: Surface Areas of Pyramids and Cones

Example:What is the surface area?

Practice 01

Lesson: Volumes of Prisms and Cylinders

Example:Find the volume of each figure. Round your answers to the nearest hundredth, if necessary.

Practice 01

Lesson: Volumes of Pyramids and Cones

Example: Find the volume of the figure below. Round your answers to the nearest hundreth, if necessary.

Practice 01

Lesson: Surface Area and Volume of Spheres

Example: What is the volume of a sphere with a diameter of 18 inches?

Practice 01

Areas and Volumes of Similar Solids

Example: The scale factor between two solid figureds is 2:5. If the surface area of the smaller solid is 45 $m^2$ , what is the area of the larger solid?