Geometry 1: 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
A ' B ' C ' is a rotation of ABC
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. For EACH of the following pairs of triangles,
explain why they are congruent and how you
know.
(a) BD bisects ABC and ADC .
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(a) Are the two triangles congruent? Explain
why or why not.
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If mA  75 and mADC  45 , find the
measurement of ABC .
mABC = ______________
(b) AC is the perpendicular bisector of DB .
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If D = 40º, find the measurement of DAB .
m DAB = ________
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.
(c) Given the following diagram, fill in the
reasons for the following proof.
Given: PM is the perpendicular bisector of XY
Prove: PX  PY
3. (a) Given the following segment AB ,
construct its perpendicular bisector. Label your
bisector HG . Label the intersection of AB and
HG point R.
Statements
Reasons
1. PM is the
perpendicular bisector of
1.
XY
2. XM  YM
2.
3. PMX  PMY
3.
4. PM  PM
4,
5.
(b). Using your construction, explain how any
point on HG is equidistant from A and B.
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PMX  PMY
6. PX  PY
5.
6.
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.
6. Given acute scalene triangle,
construct its medians.
ABC,
4. Given the following
isosceles triangle,
(a) Construct the
midpoint of AC . Label
it P.
ABP  CBP ?
Why or why not?
(b) Is
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(c) Is A  C ? Why or why not?
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5. Given the triangle below, find the value of x
and the measurement of each angle.
A 
B 
C 
1 
(b) Using your construction, define a centroid
and explain its characteristics.
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G.CO-13. Learning Target: I can make the
following formal constructions using a variety of
tools: an equilateral triangle inscribed in a
circle.
9. Given the following diagram, which of the
following statements must be true?
(Circle all that apply.)
7. Construct an equilateral triangle inscribed in
a circle. Leave all your construction marks.
(a) KJL  MLK
(b) JL  MK
(c) JLK  JKL
(d) KJ  KL
(e) JLK  MKL
10. Find the value of x and the length of BF if
CB  CD .
G-SRT.5. Learning Target:I can prove
relationships in geometric figures using
congruence criteria for triangles.
8. 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
G-SRT.8. Learning Target:I can solve real
world problems involving right triangles using
the Pythagorean Theorem.
11. 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 width of the screen?
(b) If companies price monitors by the foot, how
many feet is the monitor wide?
(c) If a company were to charge by the width of
the monitor, how much would this monitor cost
for $75.50/foot?