Geometry/Trig

Name: ______________________________

Date: _______________________________

Final Exam Review

[Unit 2: Angles and Triangles]

Types of Angles:

Types of Triangles:

By SIDES By ANGLES

Equilateral 3 sides congruent

Acute All angles less than 90°

Isosceles 2 sides congruent

Obtuse One angle more than 90°

Scalene No sides congruent

Right One right angle

(has a 90° angle)

Concept Diagram Definition

Vertical angles

Two angles across from each other when 2 lines intersect.

These angles are congruent.

Supplementary Angles

Two angles next to each other that add to 180°

(form a straight line).

Complementary Angles

Two angles that add to add to 90°.

Angles at a Point

Angles where all vertices share the same vertex.

They add to 360°.

Geometry/Trig

Fun Facts about Triangles:

All angles in a ∆ add to 180⁰

Triangle Inequality: To determine if 3 sides form a triangle… Small + Medium > Large (S + M > L)

Right Triangles must satisfy the Pythagorean Theorem: a2 + b2 = c2 (side lengths! c = hypotenuse)

Some Together: On Your Own:

1. Determine if the side

lengths given can form

a triangle. 7, 5, 4

5. Determine if the side lengths

given can form a triangle.

5, 2, 3

2. Find the missing side of the triangle:

6. Solve for the missing side of the triangle:

Steps:

1) Identify the measure of each side length and classify

them as a, b, or c.

2) Use the Pythagorean Theorem and properties of

Algebra to find the missing side.

3) Put your answer in simplest radical form, if applicable.

Geometry/Trig

3. In the diagram below, solve for the missing angle b:

Type of Angles: ___________________

b = ______________∘

7. In the diagram below, solve for the missing angle b:

Type of Angles: ___________________

b = ______________∘

4. a. What type of triangle is this? How do you know?

b. Solve for the value of y.

8. In ∆ABC, m∠A = 42° and m∠C = 63°. What is the

measure of ∠B?

9. Solve for the value of x.

Geometry/Trig

1. What is the measure of ∠𝐶?

2.

Type of Angles:

____________________________________

b = ______________∘

3.

Type of Angles:

____________________________________

b =

______________∘

Classifying Triangles:

4. Classify the following triangles according to their sides.

This triangle is a __________________

triangle, because it has

_________ congruent sides.

This triangle is a __________________

triangle, because it has

_________ congruent sides.

This triangle is a __________________

triangle, because it has

_________ congruent sides.

This triangle is a __________________

triangle, because it has

_________ congruent sides.

PRACTICE

Geometry/Trig

5. In triangle ABC, m<A = 35°, and m<C = 110°. A) Solve for the missing angle. B) What type of triangle is ∆ABC

according to its SIDES? Explain how you know.

6. Given Triangle ABC, 𝑚∡A = 30°, 𝑚∡B = 2x°, 𝑚∡C = 70°,

a. find the measurement of angle B.

b. What is the largest side of triangle ABC?

The largest side of triangle ABC is _______________ because ___________________________________

c. Is triangle ABC acute, obtuse, or right?

Triangle ABC is __________________________ because _____________________________________

Isosceles Triangle Theorem:

7. a. What type of triangle is this? How do you know?

b. Solve for the value of x.

8. a. What type of triangle is this? How do you know?

b. Solve for the value of y.

Geometry/Trig

9. In triangle XYZ, side XZ is extended to point p outside of the triangle. Solve for the angle marked b. SHOW ALL WORK! Number your steps!

Triangle Inequality Theorem:

10. For each of the following, determine if the side lengths given can form a triangle?

a) 7, 5, 4

b) 3, 6, 2

c) 5, 2, 4

d) 4ft, 108 in., 9 ft.

Pythagorean Theorem: 11. Solve for the length of side BC?

Leave your answer in simplest radical form.

Geometry/Trig 12. Does this triangle have a right angle? Explain how you know.

Mixed Theorems

13. a) In ∆ABC, m∠A = x° and m∠B = 2x+2° and m∠C = 3x+4°, what is the value of x?

b) According to its angles, what type of triangle is this?

c) What side of ∆ABC is the shortest? How do you know?

14. The accompanying diagram shows the roof of a house that is in the shape of an isosceles triangle. The vertex angle

formed at the peak of the roof is 86°.

What is the measure of angle x? Explain how you know.