# Review Multiple Choice Identify the choice that best completes

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```					Review 4

Multiple Choice
Identify the choice that best completes the statement or answers the question.
Use a protractor to classify the triangle as acute,            a. obtuse
equiangular, obtuse, or right.                                 b. right
c. equiangular and obtuse
d. equiangular and acute
1.

Find the measures of the sides of     and classify the triangle by its sides.

2.
a. equilateral                                c. scalene
b. isosceles                                  d. obtuse
Find each measure.                                            a.
b.
3.                                                                 c.
d.
2     59°

47°

1

3
64°

4.
41°
47°

2   1
66°

3

37°

a.                                            c.
b.                                            d.

5.
45°                               43°
2

39°
1

3

a.                                                       c.
b.                                                       d.

6.

55°                   2

3
28°

1
46°

a.                                                       c.
b.                                                       d.

Name the congruent angles and sides for the pair of congruent triangles.

7.
a.
b.
c.
d.
Identify the congruent triangles in the figure.                         c.
d.
8.        M                                 J
N       K

O       L

a.
b.
Determine whether                            given the coordinates of the vertices. Explain.
9.
a. Yes; Both triangles have three acute angles.
b. No; Each side of triangle PQR is not the same length as the corresponding side of triangle
STU.
c. No; Two sides of triangle PQR and angle PQR are not the same measure as the
corresponding sides and angle of triangle STU.
d. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle
STU.
Refer to the figure.                            are           c.
all isosceles triangles.
d.
X     F
14. Triangles ABC and AFD are vertical congruent
72°       M                                         equilateral triangles. Find x and y.
38°                                                      B            C

R                                                                         (2 y+ 6)°
A                                                                                  A
x+ 4             2x – 3
10. What is                    ?
a. 23                                                                         D            F
b. 38
a.
c. 42
b.
d. 35
c.
11. What is                    ?
a. 80                                                           d.
b. 38
c. 64                                                      15. Triangle RSU is an equilateral triangle.   bisects
d. 72                                                             . Find x and y.
12. If                       , what is      ?                                         R
a.     96                                                                                   ( y – 2)°
b.     124
c.     132                                                           8x + 1
d.     138
13. Triangle FJH is an equilateral triangle. Find x and               U                                 S
y.                                                                                T        5x

H
a.
(4 y – 4)°
3x – 8                                                   b.
2x – 1                           c.
d.
J                          F
16. Triangles ABC and AFD are vertical congruent
a.                                                           equilateral triangles. Find x and y.
b.
a.
B           C                                   b.
c.
2x + 9           6y°                              d.
A
5 x – 12

D           F

17. Write a flow proof for the problem.                         Prove:
X       V
Given:
Prove:
A         P
W

Z       Y
C          B         R          Q

Write a two-column proof.

18. Given: R is the midpoint of           ;             .
Prove:
S

R

V                           U

19. Given: Square GHJK
Prove:
G                           H

F

K                           J

20. Given: W is the midpoint of               and   ;       .
Review 4

MULTIPLE CHOICE

1. ANS: D
An acute triangle has 3 acute angles.
An obtuse triangle has one obtuse angle.
A right triangle has one right angle.

Feedback
A     Check for congruent sides and measure angles.
B     Check for congruent sides and measure angles.
C     Check for congruent sides and measure angles.
D     Correct!

PTS: 1               DIF: Average           REF: Lesson 4-1
OBJ: 4-1.1 Identify and classify triangles by angles.           NAT: NCTM GM.1 | NCTM GM.1a
STA: OK 1.2          TOP: Identify and classify triangles by angles.
KEY: Triangles | Classify Triangles
2. ANS: C
Use the Distance Formula to find the lengths of the sides.

If            or           or           , then the triangle is isosceles.
If                 , then the triangle is equilateral.
If neither of the above, the triangle is scalene.

Feedback
A     Use the distance formula to find the lengths of the sides.
B     Did you use the distance formula?
C     Correct!
D     What are the lengths of the sides?

PTS: 1               DIF: Average           REF: Lesson 4-1
OBJ: 4-1.2 Identify and classify triangles by sides.            NAT: NCTM GM.1 | NCTM GM.1b
STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1                         TOP: Identify and classify triangles by sides.
KEY: Triangles | Classify Triangles
3. ANS: C
The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.

Feedback
A     What do you know about vertical angles?
B     What do you know about vertical angles?
C     Correct!
D     Use the Angle Sum Theorem.

PTS: 1          DIF: Basic                      REF: Lesson 4-2    OBJ: 4-2.1 Apply the Angle Sum Theorem.
NAT: NCTM GM.1 | NCTM GM.1b                     STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1
TOP: Apply the Angle Sum Theorem.        KEY: Angle Sum Theorem
4. ANS: B
The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.

Feedback
A     Did you use the Angle Sum Theorem.
B     Correct!
C     Use the Angle Sum Theorem.
D     Use the Angle Sum Theorem.

PTS: 1                DIF: Average          REF: Lesson 4-2       OBJ: 4-2.1 Apply the Angle Sum Theorem.
NAT: NCTM GM.1 | NCTM GM.1b                 STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1
TOP: Apply the Angle Sum Theorem.           KEY: Angle Sum Theorem
5. ANS: C
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles.

Feedback
A     What is the sum of the measures of the angles in a triangle?
B     Did you use the Exterior Angle Theorem?
C     Correct!
D     Use the Exterior Angle Theorem.

PTS: 1                DIF: Average          REF: Lesson 4-2
OBJ: 4-2.2 Apply the Exterior Angle Theorem.                      NAT: NCTM GM.1 | NCTM GM.1b
STA: OK 1.2           TOP: Apply the Exterior Angle Theorem.
KEY: Exterior Angle Theorem
6. ANS: A
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles.

Feedback
A     Correct!
B     What is the sum of the measures of the angles in a triangle?
C     Did you use the Exterior Angle Theorem?
D     Use the Exterior Angle Theorem.

PTS: 1               DIF: Average          REF: Lesson 4-2
OBJ: 4-2.2 Apply the Exterior Angle Theorem.                    NAT: NCTM GM.1 | NCTM GM.1b
STA: OK 1.2          TOP: Apply the Exterior Angle Theorem.
KEY: Exterior Angle Theorem
7. ANS: C
The corresponding sides and angles can be determined from any congruence statement by following the order of
the vertices.

Feedback
A     The corresponding sides and angles can be determined from any congruence statement
by following the order of the vertices.
B     The corresponding sides and angles can be determined from any congruence statement
by following the order of the vertices.
C     Correct!
D     Did you follow the order of the vertices?

PTS: 1               DIF: Basic             REF: Lesson 4-3
OBJ: 4-3.1 Name and label corresponding parts of congruent triangles.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM GM.3                           STA: OK 1.2 | OK 1.3 | OK 3.1
TOP: Name and label corresponding parts of congruent triangles.
KEY: Corresponding Parts | Congruent Triangles
8. ANS: C
The vertices naming the triangles correspond to the congruent vertices of the two triangles in the same order.

Feedback
A     The letters naming the triangles correspond to the congruent vertices of the two
triangles.
B     Be careful with the order of the vertices.
C     Correct!
D     Are the vertices in the correct order?

PTS: 1                  DIF: Average         REF: Lesson 4-3       OBJ: 4-3.2 Identify congruent transformations.
NAT: NCTM GM.1 | NCTM GM.1b                  STA: OK 1.2 | OK 1.3
TOP: Identify congruent transformations.
KEY: Transformations | Congruence Transformations
9. ANS: D
If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are
congruent.

Feedback
A     How do you decide if two triangles are congruent?
C     Use the SSS Postulate.
D     Correct!

PTS:    1              DIF: Average             REF: Lesson 4-4
OBJ:    4-4.1 Use the SSS Postulate to test for triangle congruence.
NAT:    NCTM GM.1 | NCTM GM.1b                  STA: OK 1.2 | OK 1.3
TOP:    Use the SSS Postulate to test for triangle congruence.       KEY: SSS Postulate | Congruent Triangles
10. ANS:    B
Since         is isosceles,                   .

Feedback
A     Remember the definition of isosceles.
B     Correct!
C     Is that the base angle of an isosceles triangle?
D     Remember the definition of isosceles.

PTS:    1              DIF: Basic              REF: Lesson 4-6
OBJ:    4-6.1 Use the properties of isosceles triangles.          NAT: NCTM GM.1 | NCTM GM.1a
STA:    OK 1.2 | OK 1.3 | OK 3.3               TOP: Use the properties of isosceles triangles.
KEY:    Isosceles Triangles
11. ANS: D
Since        is isosceles,                .

Feedback
A   Is that the base angle of an isosceles triangle?
B   Remember the definition of isosceles.
C   What do you know about base angles of an isosceles triangle?
D   Correct!

PTS:   1              DIF: Basic              REF: Lesson 4-6
OBJ:   4-6.1 Use the properties of isosceles triangles.          NAT: NCTM GM.1 | NCTM GM.1a
STA:   OK 1.2 | OK 1.3 | OK 3.3               TOP: Use the properties of isosceles triangles.
KEY:   Isosceles Triangles
12. ANS:   C
;

Feedback
A   What is the sum of the base angles?
B   What is the sum of the measures of the angles in a triangle?
C   Correct!
D   Is that the vertex angle?

PTS:   1              DIF: Average            REF: Lesson 4-6
OBJ:   4-6.1 Use the properties of isosceles triangles.          NAT: NCTM GM.1 | NCTM GM.1a
STA:   OK 1.2 | OK 1.3 | OK 3.3               TOP: Use the properties of isosceles triangles.
KEY:   Isosceles Triangles
13. ANS:   B

Feedback
A   Did you set the two sides equal to each other?
B   Correct!
C   How many degrees is each angle of an equilateral triangle?
D   How many degrees is H?

PTS:   1              DIF: Basic              REF: Lesson 4-6
OBJ:   4-6.2 Use the properties of equilateral triangles.         NAT: NCTM GM.2 | NCTM GM.2a
TOP:   Use the properties of equilateral triangles.               KEY: Equilateral Triangles
14. ANS:   A

Feedback
A   Correct!
B   What do you know about the sides of an equilateral triangle?
C   How many degrees is each angle of an equilateral triangle?
D   Did you add or subtract when solving for y?
PTS:     1              DIF: Average            REF: Lesson 4-6
OBJ:     4-6.2 Use the properties of equilateral triangles.          NAT: NCTM GM.2 | NCTM GM.2a
TOP:     Use the properties of equilateral triangles.                KEY: Equilateral Triangles
15. ANS:     D

Feedback
A    Can x be negative?
B    What is the measure of TRS?
D    Correct!

PTS:     1              DIF: Average            REF: Lesson 4-6
OBJ:     4-6.2 Use the properties of equilateral triangles.          NAT: NCTM GM.2 | NCTM GM.2a
TOP:     Use the properties of equilateral triangles.                KEY: Equilateral Triangles
16. ANS:     B

Feedback
A    What is the measure of each angle in an equilateral triangle?
B    Correct!
C    Did you set the given sides equal to each other?

PTS: 1              DIF: Average            REF: Lesson 4-6
OBJ: 4-6.2 Use the properties of equilateral triangles.              NAT: NCTM GM.2 | NCTM GM.2a
TOP: Use the properties of equilateral triangles.                    KEY: Equilateral Triangles

17. ANS:
Given:
Prove:
A     P

C          B     R      Q

Proof:
A flow proof organizes a series of statements in logical order, starting with the given statements. Each statement is
written in a box with the reason verifying the statement written below the box. Arrows are used to indicate how the
statements relate to each other.
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles
are congruent.

PTS: 1                 DIF: Advanced     REF: Lesson 4-1     OBJ: 4-2.3 Solve multi-step problems.
NAT: NCTM GM.1 | NCTM GM.1b              STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1
TOP: Solve multi-step problems.          KEY: Solve multi-step problems.
18. ANS:
Sample:
Given: R is the midpoint of   ;        .
Prove:
Proof:
Statements                         Reasons
1. R is the midpoint of   .        1. Given
2.                                 2. Midpoint Theorem
3.                                 3. Given
4.                                 4. Reflexive Property
5.                                 5. SSS Postulate

PTS: 1              DIF: Basic              REF: Lesson 4-4
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
NAT: NCTM GM.1 | NCTM GM.1b                 STA: OK 1.2 | OK 1.3
TOP: Use the SSS Postulate to test for triangle congruence.       KEY: SSS Postulate | Congruent Triangles
19. ANS:
Sample:
Given: Square GHJK
Prove:
Proof:
Statements                                     Reasons
1. GHJK is a square.                           1. Given
2.                                             2. Definition of a square
3.                                             3. Definition of a square
4.                                             4. Reflexive Property
5.                                             5. SSS Postulate

PTS: 1                DIF: Basic            REF: Lesson 4-4
OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence.
NAT: NCTM GM.1 | NCTM GM.1b                 STA: OK 1.2 | OK 1.3
TOP: Use the SSS Postulate to test for triangle congruence.       KEY: SSS Postulate | Congruent Triangles
20. ANS:
Sample:
Given: W is the midpoint of    and ;               .
Prove:
Proof:
Statements                                      Reasons
1. W is the midpoint of   .                     1. Given
2.                                              2. Midpoint Theorem
3. W is the midpoint of .                       3. Given
4.                                              4. Midpoint Theoremt
5.                                              5. Given
6.                                              6. SSS Postulate

PTS:   1              DIF: Average            REF: Lesson 4-4
OBJ:   4-4.1 Use the SSS Postulate to test for triangle congruence.
NAT:   NCTM GM.1 | NCTM GM.1b                 STA: OK 1.2 | OK 1.3
TOP:   Use the SSS Postulate to test for triangle congruence.       KEY: SSS Postulate | Congruent Triangles

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