Partial Review of Chapter 4
Classify each triangle by its sides and angles.
1
2
3
4
In the following figure, name a right triangle, an acute triangle, and an obtuse triangle.
5
A triangle has angle measures of 60°, 60°, and 60°. Classify the triangle.
6
How many obtuse angles can an isosceles triangle have? How many right? How many acute?
In #7-9, find the value of
in each figure:
7
8
9
10
Find the measure of each interior angle. (Drawing is not to scale.)
11
Find the measure of each angle in this figure.
12
In the figure to the right, the value of
13
Which pair of lengths can be two of the sides of an isosceles triangle that has a perimeter of 52 inches?
is
.
A 12 inches, 22 inches B 16 inches, 21 inches C 15 inches, 22 inches D 15 inches, 25 inches
14
In the figure below, what are the values of
and ? (The figure may not be drawn to scale.)
15
The two triangle-shaped gardens depicted below are congruent. Find the missing side lengths and
angle measures.
16
If
false?
A
,
feet,
B
17
If
congruence?
, and
C
and
, which of the following statements is
D
, then
. This illustrates which property of
A Transitive B Commutative C Symmetric D Reflexive
18
If
A
, which statement is NOT true? (Hint: sketch the triangles.)
B
C
D
19
Refer to the figure below, and complete the statement.
20
Refer to the figure below. Which of the following statements is true?
A
21
A
.
by SAS B There are no congruent triangles. C
by SSS D
by SSS
Refer to the figure shown. Which of the following statements is true?
by SSS B
by SAS C
by ASA D
by SAS
22
What must be true in order for
A
B
23
by the SAS Congruence Postulate?
C
D
. Name the theorem or postulate that justifies the congruence.
A ASA B AAS C SAS D HL
24
What is the measure of each base angle of an isosceles triangle if its vertex angle measures 40 degrees
and its 2 congruent sides measure 25 units?
25
In
, AB = 3x – 2, BC = x + 4, and AC = 7. Also,
. Which term does NOT describe
A Equilateral B Acute C Isosceles D Obtuse
26
In
, if
27
Find the values of
28
Given
and
and
°, then
°.
in the diagram to the right.
;
;
;
; find
.
?
Chapter 4
Answer Section
1
ANS: Equilateral, equiangular
§4.1 Apply Triangle Sum Properties
2
ANS: Isosceles, acute
§4.1 Apply Triangle Sum Properties
3
ANS: Scalene, acute
§4.1 Apply Triangle Sum Properties
4
ANS:
5
ANS: Equiangular
§4.1 Apply Triangle Sum Properties
6
ANS: 1 obtuse; 1 right; 3 acute
§4.1 Apply Triangle Sum Properties
7
ANS: 24°
§4.1 Apply Triangle Sum Properties
8
ANS: 64
§4.1 Apply Triangle Sum Properties
9
ANS: 18°
§4.1 Apply Triangle Sum Properties
10
ANS: 91°, 61°, 28°
§4.1 Apply Triangle Sum Properties
11
ANS:
12
ANS: 101°
§4.1 Apply Triangle Sum Properties
13
ANS: C
§4.1 Apply Triangle Sum Properties
14
ANS:
15
ANS: q = 4 ft; r = 24°; s = 90°; t = 66°; u = 9.8 ft
16
ANS: C
§4.2 Apply Congruence and Triangles
17
ANS: A
§4.2 Apply Congruence and Triangles
18
ANS: C
§4.2 Apply Congruence and Triangles
19
ANS:
§§4.3 Prove Triangles Congruent by SSS
20
ANS: A
§4.4 Prove Triangles Congruent by SAS and HL
21
ANS: B
§4.4 Prove Triangles Congruent by SAS and HL
22
ANS: C
§4.4 Prove Triangles Congruent by SAS and HL
23
ANS: B
§4.5 Prove Triangles Congruent by ASA and AAS
24
ANS: 70°
§4.7 Use Isosceles and Equilateral Triangles
25
ANS: D
§4.7 Use Isosceles and Equilateral Triangles
26
ANS: 39°
§4.7 Use Isosceles and Equilateral Triangles
27
ANS:
28
ANS:
is right;
is acute;
;
;
°,
is obtuse §4.1 Apply Triangle Sum Properties
;
§4.1 Apply Triangle Sum Properties
;
§4.1 Apply Triangle Sum Properties
°
§4.2 Apply Congruence and Triangles
§4.7 Use Isosceles and Equilateral Triangles
§4.7 Use Isosceles and Equilateral Triangles