Download 4-2/4-6 Practice WS (day 1) Angles of Triangles

NAME
4-2/4-6 Practice WS (day 1)
Angles of Triangles
Triangle Angle Sum
Theorem
B
The sum of the measures of the angles of a triangle is 180.
In the figure at the right, m∠A + m∠B + m∠C = 180.
A
C
Exercises
Find the measure of each numbered angle.
S
1
Q
N
R
V
1
W
U
R
T
2
N
3
2
T
1
S
W
Q
2
P
O
Lesson
1
P
Find the measure of each angle. Define each angle measure in terms of x, then set up an
equation to solve for x.
6. In triangle DEF, m∠E is three times
m∠D, and m∠F is 9 less than m∠E.
What is the measure of each angle?
7. In triangle RST, m∠T is 5 more than
m∠R, and m∠S is 10 less than m∠T.
What is the measure of each angle?
8. In triangle JKL, m∠K is four times
m∠J, and m∠L is five times m∠J.
What is the measure of each angle?
9. In triangle XYZ, m∠Z is 2 more than twice
m∠X, and m∠Y is 7 less than twice m∠X.
What is the measure of each angle?
Chapter 4
11
Geometry
NAME
4-2
Study Guide and Intervention(continued)
Angles of Triangles
Exterior Angle
Theorem
The measure of an exterior angle of a triangle is equal to
the sum of the measures of the two remote interior angles.
m∠1 = m∠A + m∠B
B
1
A
C
D
Exercises
Find the measures of each numbered angle.
A
X
2 1
1
Y
Z
C
W
D
Find each measure.
12. m∠ABC
13 . m∠F
A
E
x°
95°
C
D
H
G
F
Isosceles triangle: _____________________________________________________
Parts of an isosceles triangle
P
Legs: The two congruent sides of an isosceles triangle
Vertex: The point where the two congruent sides touch
Base: The side across from the vertex
Vertex angle: The angle across from the base
Base angle: An angle across from a leg of an isosceles triangle.
R
Q
Use 𝛥PRQ above to answer the following.
14. Name the legs
17. Name the vertex angle
Chapter 4
15. Name the vertex
16. Name the base
18. Name the base angles
12
Geometry
The Isosceles Triangle Base angle theorem: If a triangle is isosceles, then its base angles are
congruent.
Abbreviated: ________________________________________________________________
Converse of The Isosceles Triangle Base angle theorem: If a triangle has congruent base angles,
then the triangle is isosceles.
Abbreviated: ________________________________________________________________
ALGEBRA Find the value of each variable. Justify your answer.
20. S
R
19.
P
W
V
40°
2x°
3x – 6
T
Q
B 2x°
22.
21.
2x + 6
23.
Y
3x°
Z
24.
N
T
3x°
M
A
)°
5x°
R
O
S
C
Equilateral triangle: _______________________________________________________
*Because an equilateral triangle is really isosceles, we know two things:
1. A triangle is equilateral if and only if it is equiangular.
2. Each angle of an equilateral triangle measures 60°.
ALGEBRA Find the value of each variable.
D
25.
27. L
26.
6x – 5
F
6x°
E
J
5x
3x°
H
M
28. PROOF Write a two-column proof.
Given: ∠1 ≅ ∠2
Prove: 𝐴𝐵 ≅ 𝐶𝐵
A
1
3
C
D
2
E
K