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Name ____________________________________________
Date______________
Period ________
Geometry with Trig
Unit 4 Test Review
Use the diagram on the right for problems 1 & 2.
1. Find the measure of each angle and write them ON the diagram. Then write them on the lines provided.
a. mD  __________
d. mBCA  ________
b. mDCA  ________
e. mB  ________
c. mDAC  ________
f. mBAC  ________
2. Use the labeled diagram to classify each triangle by its angles and sides.
a. ΔABC: _________________ ,_____________________
b. ΔACD: _________________ ,_____________________
c. ΔBAD: _________________ ,_____________________
3. Use the given diagram to find the side lengths or angles measures.
a. Given: ΔFGH is an equilateral triangle.
b.
m1  _______˚
FG = ________
m2  _______˚
GH = ________
m3  _______˚
FH = ________
m4  _______˚
4. Complete each statement below with sometimes, always, or never true. (Hint: Sketch diagrams OR replace the last
word of the sentence with its definition and read the statement again.)
a. Equiangular triangles are _________________ right triangles.
b. Equilateral triangles are _________________ isosceles.
c. Right triangles are _______________ acute.
d. Acute triangles are ________________ isosceles.
5. Find the value of x and/or y. Be sure to mark your diagram! Show all work, including an algebraic equation.
a.
b.
y˚
50˚
c.
d.
e.
f.
(9y)˚
(2x + 5)˚
(3x – 15)˚
6. Draw an example of each type of triangle below, if possible. Be sure to mark the diagram. If not possible,
explain why not.
a. Right scalene
b. Right isosceles
c. Obtuse isosceles
d. Obtuse equilateral
7. If AD is an altitude of ABC, which 8. Which of the following do NOT
represent the side lengths of a
of the following must be true?
triangle?
(Draw a diagram to help!)
A. AD  DC
9. A(n) ___________ is a segment that
contains a vertex of a triangle and
the midpoint of the opposite side.
A. 7, 11, 5
A. altitude
B. BD  DC
B. 8, 9, 9
B. angle bisector
C. ADC is a right angle
C. 7, 8, 2
C. median
D. BAD  CAD
D. 12, 6, 6
D. perpendicular bisector
For #10-11, be sure to mark the diagram!
10. If AD is an altitude of ABC, find the perimeter of
ABC.
(12x – 9) ft.
A
(15x + 45)°
11. If GF is a median of GIT, find I.
G
C
(10x – 9) ft.
I (x + 3) in. F (2x – 6) in. T
15
D
9
B
12. Circle the sets of numbers that can represent the side lengths of a triangle. There are more than one!
13 ft, 43 ft, 37 ft
8 in, 23 in, 9in
2 cm, 2 cm, 1 cm
1 ft, 24 in, 18 in
6 m, 8 m, 14 m
5 km, 5 km, 5 km
13. What is the range of possible lengths for the third side?
14. In ΔRQP, QP = 15 ft, RP = 25 ft, and RQ = 13 ft.
Order the angles from smallest to largest.
4.5
12
15. Given that three side lengths of a triangle are 13 in., (2x – 4)
in., and 7 in., find all possible values of x.
16. Using ∆ABC, order the sides from largest to
smallest.
A
75 C
36
B
Matching: Use the diagram to match the segment with the correct vocabulary word.
______ 17. Perpendicular bisector
A. AD
______ 18. Angle bisector
B. CH
______ 19. Median
C. EB
______ 20. Altitude
D. FG
21. Triangle ABC has vertices at A(2, 8), B(8, 6), and C(4, 2). Plot the points and then draw in the specified segment. Be
sure to label your diagram with ALL information!
a) Draw the perpendicular bisector of AB.
b) Draw the median from B.
c) Draw the line containing the altitude from A.