Download Types of Angles

Geometry/Trig
Name: ______________________________
Date: _______________________________
Lesson 13-2: Final Exam Review
[Unit 3 Angles and Triangles]
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The learning goals we achieved in these units were…
What are right, acute, and obtuse angles?
How can we use special angle pair definitions to solve for missing angles?
How do you classify the different types of triangles by sides?
What is the Side-Angle Relationship in triangles?
What is the Triangle Inequality Theorem? What does the Triangle Inequality Theorem help us to conclude?
What is the Pythagorean Theorem? For which type of triangle does the Pythagorean Theorem apply?
What is the isosceles triangle theorem
Key Ideas:
The Pythagorean Theorem
What is the Pythagorean Theorem?
What does each letter represent?
Side-Angle Relationship
--The ___________side is across from
the______________ angle.
--The ______________ side is across from
the ______________ angle.
--The ______________ side is across from
What type of triangles do we use this with? the ______________ angle.
Isosceles Triangles
Triangle Properties
--All angles in a triangle add to __________.
Isosceles triangles are triangles with two
congruent ______________.
How do we identify which two angles are
congruent to each other?
--Classifying but sides:
Scalene ( _____ sides are congruent)
Equilateral( _____ sides are congruent)
Isosceles( _____ sides are congruent)
Triangle Inequality:
The sum of the two _________________________
Sides must be _______________________ than the
third side.
--Classifying by angles:
Acute (all angles are __________ 90)
Obtuse (one angle is __________ 90)
Right (one angle is __________ 90)
Geometry/Trig
Concept
Diagram
Vertical angles
Supplementary Angles
Complementary Angles
Adjacent Angles
Angles at a Point
Definition
Two angles ____________________ each
other when 2 lines _______________.
Two angles that add to
_______________.
Two angles that add to
_______________.
Two angles who share a common
________ and a common ________ (“next
to”)
Angles where all vertices share the same
___________. Their sum is
____________.
Guided Example:
Find the missing side
of the triangle:
1) a = 5, b = x, c = 13 (c is always the hypotenuse)
2)
.
c2 = a2 + b2
132 = 52 + x2
169 = 25 + x2
x2 = 144
√𝑥 2 = √144
x = 12
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
Practice Section by Topic:
Types of Angles:
1.
Type of Angles: _____________________________________
b = ______________∘
2.
Type of Angles: _____________________________________
b = ______________∘
3.
Type of Angles: _____________________________________
b = ______________∘
4.
Type of Angles: _____________________________________
b = ______________∘
5.
Type of Angles: _____________________________________
b = ______________∘
Geometry/Trig
Properties of Triangles:
6. What is the measure of ∠𝐶?
7. In ∆ABC, m∠A = 42° and m∠C = 63°. What is the measure of ∠B?
8. In ∆ABC, m∠A = x° and m∠B = 2x+2° and m∠C = 3x+4°, what is the measurement of ∠B?
Classifying Triangles:
Classify the following triangles according to their sides.
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This triangle is a __________________ triangle, because it has
_____________________________
This triangle is a __________________ triangle, because it
has _____________________________
This triangle is a __________________ triangle, because it has
_____________________________
This triangle is a __________________ triangle, because it
has _____________________________
Geometry/Trig
9. In triangle ABC, m<A = 35°, and m<C = 110°. What type of triangle is triangle ABC in terms of its SIDES? How do you
know?
10. Given Triangle ABC, 𝑚∡A = 30°, 𝑚∡B = 2x°, 𝑚∡C = 70° find the measurement of angle B.
a. What is the largest side of triangle ABC?
 The largest side of triangle ABC is _______________ because ___________________________________
b. Is triangle ABC acute, obtuse, or right?
 Triangle ABC is __________________________ because _____________________________________
Isosceles Triangle Theorem:
11. What type of triangle is this? How do you know?
a.
Solve for the value of x
12. What type of triangle is this? How do you know?
a. Solve for the value of y.
Geometry/Trig
13. In triangle XYZ, side XZ is extended to point p outside of the triangle. Solve for the angle marked b.
Explain your steps.
I know angle Y = ________ because …
I know ∠𝑌𝑍𝑋 = _______ because…
I know ∠𝑃𝑍𝑌 = ______ because…
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.
Triangle Inequality Theorem:
For each of the following, determine if the side lengths given can form a triangle?
15.
17.
7, 5, 4
5, 2, 4
16.
18.
3, 6, 2
4ft, 108 in., 9 ft.
Geometry/Trig
Pythagorean Theorem:
19. If (16, 30, y) are the sides of a right triangle, where y is the largest side, what is the value of y? Leave your answer in
simplest radical form, if necessary.
20. Solve for the length of side BC? Leave your answer in simplest radical form.
21. Does this triangle have a right angle? Explain how you know.
22. 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?