Download Triangle Congruence REVIEW Name Geometry 1 Geometry 1

Triangle Congruence REVIEW
Geometry 1
Name
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.
4. Find the measurement of  Z.
z
x
28˚
35˚
1. Given that DEF is a translation of ABC,
explain why E is congruent to B.
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2.MNP and QNP have the following
properties: PN is the perpendicular bisector of
MQ .
M
N
Q
w
y
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. (a) Given the following segment AB ,
construct and name its perpendicular bisector.
P
(a) Why are the 2 triangles congruent? ________
(b) If MN = 4, MP = 13, QN = x + 2, and
QP = y – 1, determine the values of x and y.
a.
b.
x = 5, y = 14
x = 2, y = 14
c.
d.
x = 2, y = 12
x = 4, y = 13
G-CO.8. Learning Target: I can explain which
series of angles and sides are essential in order
to show congruence through rigid motions
3. Which CAN be used to justify that the two
triangles are congruent?
(b). Based on your construction above, explain
the characteristics of perpendicular bisectors.
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a. SSS b. SAS c. AAS d. ASA
Geometry 1: Triangle Unit Test REVIEW
10/10/13
PUHSD Geometry Curriculum Team
Page 1 of 4
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 the two triangles below, answer the
following questions
6. Given the following diagram, fill in the
reasons for the following proof.
Given: PX  PY , PM is the perpendicular
bisector of XY
Prove: X  Y
(a) Are the two triangles congruent? Why or
why not?
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(b) Can you conclude that C  F ? Why or
why not?
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6.
Geometry 1: Triangle Unit Test REVIEW
10/10/13
PUHSD Geometry Curriculum Team
8. Given acute scalene triangle,
construct the medians.
ABC,
G.CO-13. Learning Target: I can make the
following formal constructions using a variety of
tools: an equilateral triangle inscribed in a
circle.
10. Tyler is using a compass and straightedge to
inscribe an equilateral triangle inside circle O.
His first step is to draw diameter PQ . Describe
Tyler’s next step in the construction.
P
Q
O
(b) Using measurements from one of the
medians you constructed above define a centroid
and explain its characteristics.
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a. Draw two more diameters that divide the
circle into six equal pieces.
b. Open the compass to a width of PQ, put the
compass point on P (or Q), and draw an arc that
intersects the circle.
c. Open the compass to a width greater than OQ,
place the compass point at P and draw an arc.
Then place the compass point at Q and draw an
arc. Then use the intersections of the two arcs to
draw a perpendicular bisector of
.
d. Open the compass to a width of OQ, put the
compass point on P (or Q), and draw an arc that
intersects the circle.
9. Given that CBF  CDF , find the
measurement of BF.
G-SRT.5. Learning Target: I can prove
relationships in geometric figures using
congruence criteria for triangles.
11. If ABC  CDA , which of the following
must be true?
a. AB  CA
b. BC  DC
c. CAB  ACD
d. ABC  CAD
Geometry 1: Triangle Unit Test REVIEW
10/10/13
PUHSD Geometry Curriculum Team
12. Is there enough information given to prove
that the following pairs of triangles are
congruent? Explain why or why not. If not,
describe what information could be added to
guarantee congruence.
G-SRT.8. Learning Target: I can solve real
world problems involving right triangles using
the Pythagorean Theorem.
13. A kite frame consists of two pieces of wood
placed along the diagonals. Decorative binding
will be placed along the perimeter of the kite.
If the binding costs $1.50 a foot, what will be
the total cost?
HINT: there are 12 inches in a foot.
Geometry 1: Triangle Unit Test REVIEW
10/10/13
PUHSD Geometry Curriculum Team