# Geometry Help | Free Geometry Lessons & Practice Problems

Go through the lessons and practice problems below to help you learn Geometry and excel in school. We’ll track your progress and help you identify your strengths and weaknesses. Geometry help is available to everyone, but you need to create an account in order to access the practice questions and track your progress.

#### 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.

### Lesson: Proving Lines Parallel

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

### Lesson: Triangle Angle Sum and Exterior Angle Theorem

*Example:*Find the measure of each angle indicated.

### Lesson: Equations of Lines in the Coordinate Plane

*Example:* Sketch the graph of the line

### 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 .

#### II. Congruent Triangles

### Lesson: Congruent Triangles

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

### Lesson: Triangle Congruence by SSS and SAS

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

### Lesson: Triangle Congruence by ASA and AAS

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

### Lesson: Identifying Corresponding Parts of Congruent Triangles

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

### Lesson: Isosceles and Equilateral Triangles

*Example:* In ,

Which of the following statements is true?

*Example:* In , . If the measure of is 50 degrees, and the measure of is degrees, what is the value of ?

### Lesson: Triangle Congruence by HL (Right Triangles)

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

### Lesson: Congruence in Overlapping Triangles

*Example:* Given: , what postulate will prove ?

#### III. Relationships with Triangles

### Midsegments of Triangles

*Example:* Find the length of *VU*

### Angle Bisectors in Triangles

*Example:* Find the missing length indicated.

### Bisectors in Triangles

*Example:* Find the measure of the indicated length.

### Medians and Altitudes

*Example:* What is the measure of ?

### Indirect Proofs

*Example:*What is the first step to this indirect proof?

is acute

### Lesson: Inequalities in a Triangle

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

### Inequalities in Two Triangles

*Example:*

What theorem can be used to prove ?

#### IV. Polygons and Triangles

### Lesson: Angle Sum Theorem for Convex Polygons

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

### Lesson: Properties of Parallelograms

*Example:* Find the measurement indicated in the parallelogram.

### Proving that a Quadrilateral is a Parallelogram

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

### Properties of Rhombuses, Rectangles, and Squares

### Lesson: Rhombuses

### Lesson: Rectangles

### Lesson: Squares

*Example:* Which figure below is a rhombus?

### Conditions of Rhombuses, Rectangles, and Squares

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

### Trapezoids and Kites

### Polygons in the Coordinate Plane

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

### Applying Coordinate Geometry

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

### Proofs Using Coordinate Geometry

*Example:* Which theorem can be used to proved ?

### Solving Proportions

*Example:* Solve for

### Similar Polygons and Proportions

*Example:* Solve for

### Proving Triangles Similar

*Example:*Given , which theorem can be used to prove

### Similar Right Triangles

*Example:* Solve for

### Proportions in Triangles

*Example:*Find the missing length indicated

#### 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?

### 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?

### Lesson: Trigonometry

*Example:* Right triangle has the following side lengths: is 8 ft, is 3 ft. What is tan(A)?

### 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.

### Law of Sines

*Example:* In , the length of is 12 yd, the length of is 24 yd, and the measure of angle A is 30 degrees. What is the measure of angle B?

### Law of Cosines

*Example:* In , the length of is 11.3 yd, the length of is 19.9 yd, and the measure of angle C is 112.4 degrees. What is the length of ?

#### VII. Transformations

### Lesson: Translations

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

### Reflections

### Lesson: Reflection Over an Axis

### Lesson: Reflection Over a Horizontal or Vertical Line

### Lesson: Reflection Over the Line *y=x*

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

### Lesson: Rotations

*Example:* 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 ?

### Compositions of Isometries

*Example:* What are the coordinates of the point after ?

### Congruent Triangles and Congruence Transformations

*Example:*

### Lesson: Dilations

*Example:* Triangle , , becomes triangle , , under a dilation. What would the scale factor be for this dilation?

### Similarity Transformation

*Example:* When equilateral triangle is dilated by a factor of , what are the corresponding angle measurements of the image triangle?

#### 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?

### 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?

### 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?

### 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?

### Trigonometry and the Area of Regular Polygons

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

### Arc Measures and Arc Lengths in Circles

*Example:* Find the measure of *arc JK*

### Sector Area

*Example:* Find the area of each sector.

### 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 if necessary.

#### 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.

### Lesson: Surface Areas of Prisms and Cylinders

*Example:* Sketch the net of the solid below

### Lesson: Surface Areas of Pyramids and Cones

*Example:*What is the surface area?

### Lesson: Volumes of Prisms and Cylinders

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

### Lesson: Volumes of Pyramids and Cones

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

### Lesson: Surface Area and Volume of Spheres

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

### 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 , what is the area of the larger solid?

#### X. Circles

### Lesson: Tangent Lines

*Example:* Can a radius be drawn to a point of tangency?

### Lesson: Congruent Chords

### Lesson: Intersecting Chords (Segment Lengths)

*Example:* Two chords intersect and shown in the diagram below. What is the value of ?

### Lesson: Secants and Tangents w/ Vertex Outside of Circle (Segment Lengths)

*Example:* Solve for in the figure below.

### Lesson: Central Angles, Inscribed Angles, and Arcs

*Example:* Find the measure of the arc or angle indicated.

### Lesson: Intersecting Chords (Arc and Angle Measures)

*Example:* Find the measure of the indicated angle formed by the intersecting chords.

### Lesson: Tangent and Secant Lines w/ Vertex Outside of Circle (Arcs & Angles)

*Example:*

### Lesson: Chords Perpendicular to a Radius (Segment Measures)

*Example:* Solve for .

### Lesson: Equation of a Circle

*Example:* Use the information provided to write the equation of each circle.

Center: (-4, 8)

Radius: 3

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