Download Unit 5 Test A

Name ____________________
Unit 5 Test – Geometry
Period _____
1. Given that point A is located on the line segment BC, which statement must be true?
A) AB + BC = AC B) BA + AC = BC C) AB = BC D) BA = AC
2. In parallelogram ABCD, diagonals AC and BD intersect at point E. Which statement is always true?
A) Triangle AED is isosceles.
B) Triangle ABD is a right triangle.
C) Triangle AEB is congruent to triangle AED.
D) Triangle ABC is congruent to triangle CDA.
3. If the midsegment of an equilateral triangle is 6 inches long, find the
perimeter of the triangle.
A) 12 inches
B) 18 inches
C) 36 inches
D) 48 inches
4. Triangle ABC is similar to triangle DEF. Which statement is false?
A) <ABC ≅ <EDF
B) AC : DF = BC : EF
C) m<ACB = m<DFE
D) AB : BC = DE : EF
5. The accompanying diagram shows how ΔA’B’C’ is constructed to be similar to ΔABC. Which
statement proves the construction?
A) If two triangles are congruent, then they are similar.
B) The two triangles are similar, then the angles of one triangle are congruent to the corresponding
angles of the other triangle.
C) Two triangles are similar if two angles of one triangle are congruent to two angles in the other
triangle.
D) The corresponding sides of two triangles are proportional.
5. Given the following diagram, which statement cannot be proven true?
A) <ACB is a right angle. B) m<CAB + m<CBA = 900
̂ = 1800
C) m 𝑨𝑩
D) AC = AB
6. In isosceles ΔABC with vertex angle A, m<B is
20 more than twice the measure of m<A.
What is the measure of <C?
7. To maintain the structural integrity of a new office building, an architect needs to create similar
triangles. His blueprint names the similar triangles ΔABC and ΔDEF. If m<A = x2 – 8x, m<C = 4x – 5,
and m<D = 5x + 30, find the measure of <C that would make the triangles similar.
8. The radius of circle G is 10 cm long. The radius is the perpendicular bisector
of a chord in the circle at a point H 6 cm from point G. How long is the chord?
9.
If the radius of circle O is 9 in. and PR = 27 in.,
how long is TR to the nearest tenth of an inch?
a) 16.5 in. b) 19.5 in. c) 25.5 in.
d) 28.5 in.
Use the circle below to answer questions #10 – 12. Assume that GE = 22 cm and m<DPG = 1280.
10. What is the degree measure of arc DE?
11. What is the length of arc DE?
12. What is the area of the sector bounded by PD and PE?
13. Which statement would NOT prove these triangles congruent?
A) <C = <E
C) AB = DF
14. What postulate proves ΔABC =
̃ ΔDBC?
A) SSS B) SAS C) ASA D) AAS E) HL
16. Given: ABCD is a parallelogram.
Prove: AC bisects BD.
B) <A = <D
D) AC = DF
15. What statement would prove ΔABC ~ ΔDFE?
A) AC = DF B) <F = <D C) <E = <C D) AB = DE
Statement
Reason
1. ABCD is a parallelogram.
1. A) ________________
2. AB // CD
2. B) ________________
3. <ABE = <CDE
3. C) ________________
4. <AEB = <CED
4. D) ________________
5. AB = CD
6. ΔABE = ΔCDE
5. Opposite Sides of a
Parallelogram are Equal
6) E) ________________
7. BE = DE
7) F) ________________
8. AC bisects BD.
8) Definition of Bisector
Tasks
I. Prove, using a two column or paragraph proof, that each point
on the perpendicular bisector of a segment is the same distance
from the endpoints of the segment.
Given: CD is the perpendicular bisector of AB.
Prove: AD = BD
II. Farmer Joe decides to plant corn, his most profitable plant, on a
1400 sector of his circular plot of land. The radius of the entire
plot is 80 yards. Show your equations/work for each section.
a) Joe wants to fence in his corn so the deer can’t eat it. How many
yards of fence will he need? (Hint: Don’t forget the straight sides.)
b) What area will the corn take up?
c) If each square yard holds about 8 corn stalks, about how many stalks of corn will Farmer Joe
produce?
Tasks
I. Prove, using a two column or paragraph proof, that each point
on the perpendicular bisector of a segment is the same distance
from the endpoints of the segment.
Given: CD is the perpendicular bisector of AB.
Prove: AD = BD
II. Farmer Joe decides to plant corn, his most profitable plant, on a
1400 sector of his circular plot of land. The radius of the entire
plot is 80 yards. Show your equations/work for each section.
a) Joe wants to fence in his corn so the deer can’t eat it. How many
yards of fence will he need? (Hint: Don’t forget the straight sides.)
b) What area will the corn take up?
c) If each square yard holds about 8 corn stalks, about how many stalks of corn will Farmer Joe
produce?