Download Geometry Module 4 Lesson 19 – Applying Triangle Congruence

Geometry Module 4 Lesson 19 – Applying Triangle Congruence Relationships
Assessment Test Answers
1. Given two scalene triangles,
A. ̅̅̅̅
̅̅̅̅
Incorrect. This is a true statement
B.
C. ̅̅̅̅
, which of the following is NOT True:
Incorrect. This is a true statement
̅̅̅̅
Incorrect. This is a true statement
Correct. Based on the notation used in naming the triangle,
meaning
is congruent to
and not
.
D.
by SAS. He knows F is the midpoint of ̅̅̅̅ , what else does
2. Juan is to proving
he need to know?
D
E
L
F
A.
B. ̅̅̅̅
̅̅̅̅
C.
D. ̅̅̅̅
,
̅̅̅̅
K
Incorrect. This is given as right angles in the picture and is angle of the SAS
proof.
Correct. Since F is a midpoint ̅̅̅̅ ̅̅̅̅ and
, the side needed
is ̅̅̅̅
̅̅̅̅
Incorrect. The right angle is the given angle and the needed angle to
prove SAS.
Incorrect. This is already given because the segments are created by the
midpoint of ̅̅̅̅.
3. Based on the information shown in the figure, which theorem proves
?
M
N
Q
P
A. Side-Side-Side (SSS)
B. Side-Angle-Side (SAS)
C. Hypotenuse Leg (HL)
D. Angle-Angle-Side (AAS)
4. Given
;
Incorrect. Based on the markings given in the figure,̅̅̅̅̅ ̅̅̅̅,
because they are right angles and ̅̅̅̅̅ ̅̅̅̅̅ by
the reflexive property, this is not SSS.
Correct. Based on the markings given in the figure,̅̅̅̅̅ ̅̅̅̅ ,
because they are right angles and ̅̅̅̅̅ ̅̅̅̅̅ by
the reflexive property, the triangles are congruent by SAS.
Incorrect. Based on the markings given in the figure,̅̅̅̅̅ ̅̅̅̅,
because they are right angles and ̅̅̅̅̅ ̅̅̅̅̅ by
the reflexive property, this is not HL.
Incorrect. Based on the markings given in the figure,̅̅̅̅̅ ̅̅̅̅,
because they are right angles and ̅̅̅̅̅ ̅̅̅̅̅ by
the reflexive property. It isn’t possible to find corresponding
congruent acute angles in this figure so AAS isn’t going to work.
and ̅̅̅̅
̅̅̅̅ . Find the length of ̅̅̅̅ .
by AAS, thus ̅̅̅̅
.
A. 10 inches
Correct.
Since ̅̅̅̅
B. 12 inches
Incorrect. This is the length of ̅̅̅̅ .
C. 14 inches
D. There is not enough information to
determine the length
̅̅̅̅
̅̅̅̅ by CPCTC.
Incorrect.
by AAS, thus ̅̅̅̅ ̅̅̅̅ by CPCTC
̅̅̅̅
and
, therefore ̅̅̅̅̅
.
Incorrect. There is enough information to conclude
.
5. Identify the correct statement of congruence based on the two triangles in the figure below:
Q
J
K
R
Incorrect.
.
Incorrect.
.
is not congruent to
because
is not congruent to
is not congruent to
because
is not congruent to
Incorrect. This is the same triangle.
Correct. Based on the notation, all of the parts of both triangles correspond to each
other.