Download Geo B Chapter 4 Review - smilardo

Geometry B
Name: ______________________
Date: ____________
Block: ____________
Triangle Congruence Chapter 4 Review
All work must be shown for credit.
Sections 4.1 - 4.6 and 4.8.
Define the following terms:
acute triangle
auxiliary line
base angle
congruent polygons
corresponding angles
corresponding sides
CPCTC
equiangular triangle
equilateral triangle
exterior angle
included angle
included side
interior angle
isosceles triangle
legs of an isosceles triangle
obtuse triangle
remote interior angle
right triangle
scalene triangle
triangle rigidity
vertex angle
Tell whether each statement is sometimes, always, or never true. Support your
answer with a sketch.
22) An acute triangle is a scalene triangle.
23) A scalene triangle is an obtuse triangle.
24) An equiangular triangle is an isosceles triangle.
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25) Classify each triangle by its angle measures.
△BEA
26) Classify each triangle by its side lengths.
△PST
△RSP
△DBC
△ABC
△RPT
27) Find the side lengths of each triangle.
28) An isosceles triangle has a perimeter of 34 cm. The congruent sides measure (4x - 1)
cm. The length of the third side is x cm. What is the value of x?
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29) The base of the Flatiron Building is a triangle bordered by three streets: Broadway,
Fifth Avenue, and East Twenty-Second Street. The Fifth Avenue side is 1 ft. shorter
than twice the East Twenty-second Street side. The East Twenty-second Street side
is 8 ft. shorter than half the Broadway side. The Broadway side is 190 ft.
a. Find the two unknown side lengths.
b. Classify the triangle by its side lengths.
30) Find m∠S
31) Find m∠N.
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32) Given: RS ≅ UT, and VS ≅ VT. V is the midpoint of RU.
Prove: △RSV ≅ △UTV
33) Given: AB ≅ DE, DB ≅ AE
Prove: △ADB ≅ △DAE
34) Show and explain that △ADB ≅ △CDB when s = 5.
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35) Given: C is the midpoint of AG, HA  GB
Prove: ∆HAC  ∆BGC
36) Given: WX ⊥ XZ , YZ ⊥ ZX , WZ  YX
Prove: ∆WZX  ∆YXZ
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37) Given: PQ  RQ PS  RS
Prove: QS bisects ∠PQR
38) Given: E is the midpoint of AD and BC
Prove: △ABE and △DCE
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Indicate whether the two triangles shown are congruent by SSS, ASA, SAS, AAS or HL.
If there is not enough information given, write “not possible”.
39)
40)
41)
42)
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43) Find the m∠N and m∠P.
44) The measure of one of the acute angles in a right triangle is given What is the measure
of the other acute angle?
56.8°
4y°
45) Find the measure of each angle.
46)
For Triangle ABC and Triangle XYZ, mA = mX and mB = mY. Find the measure
of C and Z if mC =(4x + 7)° and mZ = 3(x + 5) °. What theorem did you use to
solve this problem?
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47) Find the measure of all angles.
48) Find the length of BC.
49) A plane is flying parallel to the ground along AC. When the plane is at A, an air-traffic
controller in tower T measures the angle to the plane as 0°. After the plane has
traveled 2.4 mi to B, the angle to the plane is 80°. How can you find BT?
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