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Geometry 1H: Triangle Congruence
Unit Review
G-CO.7. Learning Target: I can show that two
triangles are congruent through rigid motions if and
only if the corresponding pairs of sides and
corresponding pairs of angles are congruent.
1. Given that
ABC
A ' B ' C ' is a rotation of
Name ______________________________________
Period _______________ Date _________________
G-CO.8. Learning Target: I can explain which
series of angles and sides are essential in order
to show congruence through rigid motions
2. (a) Given that BD bisects ABC and
ADC , explain why BAD  BCD .
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(b) If mA  75 and mADC  45 , find
the measurement of ABC .
(a) Are the two triangles congruent? ______
(b) Explain why or why not.
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2. Using the diagram below, describe one way
to map ABE onto CDE .
mABC = ______________
3. What additional information would you
need to prove that the two triangles shown
are congruent?
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If mA  (3x  5) and mC  (5 x  17) :
Find the value of x. _________
Find mA _____________
Geometry 1: Triangle Unit Test REVIEW
6/6/16
PUHSD Geometry Curriculum Team
Page 1 of 5
G-CO.9. Learning Target: I can prove the
following theorem in narrative paragraphs, flow
diagrams, in two column format, and/or using
diagrams without words: points on a perpendicular
bisector of a line segment are exactly those
equidistant from the segment’s endpoints. I can make
the following formal constructions using a variety of
tools: constructing perpendicular bisectors.
5. Given the following segment AB , construct
its perpendicular bisector. Label your bisector
HG . Label a point M anywhere on HG such
that M is NOT at the intersection of AB and
HG .
4. Given the following diagram, fill in the
reasons for the following proof.
Given: PM is the perpendicular bisector of XY
Prove: PX  PY
(b). Using your construction, explain why point
M is equidistant from A and B.
Statements
Reasons
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1. PM is the
perpendicular bisector
of XY
1.
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2. XM  YM
2.
3. PMX  PMY
3.
4. PM  PM
4.
5.
PMX  PMY
6. PX  PY
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5.
6.
Geometry 1H: Triangle Unit REVIEW
6/6/16
PUHSD Geometry Curriculum Team
Page 2 of 5
G-CO.10. Learning Target: I can prove the
following theorems in narrative paragraphs,
flow diagrams, in two-column format, and/or
using diagrams without words: measures of
interior angles of a triangle sum to 180°; base
angles of isosceles triangles are congruent; the
medians of a triangle meet at a point.
7. Given acute scalene triangle,
construct the medians.
ABC,
6. Given the following
isosceles triangle, explain
the theorem that “if two
sides of a triangle are
congruent, then the angles
opposite those sides are
congruent.”
(b) Using your construction, define a centroid
and explain its characteristics.
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8. Given the triangle shown below.
6. Given the triangle below, find the value of x
and the measurement of each angle.
(a) What type of triangle is this?
_________________
A 
B 
C 
(b) List 2 properties for this type of triangle.
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1 
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(c) Find the value of x. _______
Geometry 1H: Triangle Unit REVIEW
6/6/16
PUHSD Geometry Curriculum Team
Page 3 of 5
G.CO-13. Learning Target: I can make the
following formal constructions using a variety of
tools: an equilateral triangle inscribed in a
circle.
11. Use the diagram below to answer the
following questions.
9. Construct an equilateral triangle inscribed
in a circle. Leave all your construction
marks.
Part A: Are the two triangles congruent? If
so, state how. If not, what additional
information do you need?
Part B: Is KJL  LMK ? How do you
know?
G-SRT.5. Learning Target: I can prove
relationships in geometric figures using
congruence criteria for triangles.
10. If ABC  CDA , which of the
following must be true? (Circle all that
apply.)
a. AB  CA
b. BC  DA
c. CAB  ACD
d. ABC  CAD
Part C: If mMLK = (7x + 4)° and
mJKL = (5x + 30)°, what is the value of
x?
Part D: What is the mMLK ?
Part E: If mMKL is 21°, what is the
measure of KML ?
Part F: What is the measure of JLK ?
Geometry 1H: Triangle Unit REVIEW
6/6/16
PUHSD Geometry Curriculum Team
Page 4 of 5
G-SRT.8. Learning Target: I can solve real
world problems involving right triangles using
the Pythagorean Theorem.
12. In a computer catalog, a computer monitor is
listed as being 19 inches. This is the diagonal
distance across the screen. The screen itself
measures 10 inches in height.
(a) What is the length of the screen?
(b) If companies price monitors by the foot, how
many feet is the monitor long?
(c) If a company were to charge by the length of
the monitor, how much would this monitor cost
for $75.50/foot?
Geometry 1H: Triangle Unit REVIEW
6/6/16
PUHSD Geometry Curriculum Team
Page 5 of 5