Download Math 1312 Test 2 Review Questions Test 2 covers chapters 3 and 4

Math 1312 Test 2 Review Questions
Test 2 covers chapters 3 and 4 from the textbook.
How to study: Study the class notes, review homework problems, and try to do as many
exercises as you can from the textbook. Note that answers are provided at the back of the book to
all odd numbered problems.
You need to know what definitions mean and theorems and postulates as facts but you do not
need to memorize them word by word.
Here I provide some examples for you. This is not a complete list, studying only these examples
is not enough!
1. It is given that ∆
≅∆
a) If ∠
37 and
b) If
7.3 ,
.
∠
68 , find
4.7 , and
∠ .
6.3
, find
.
2.
a) Use ONLY the given information to state the reason why ∆
≅∆
.
≅
(Identity).
∠ ≅∠ ,∠
≅∠
, and
b) What additional parts needed to prove ∆
≅∆
by ASA if we know that
∠ ≅ ∠ and ∠
≅∠
?
C
A
B
D
3. Given ∆
with
≅
and
∠
69 , find
∠ . Draw a picture!
4. Given ∆
with
≅
and
∠
40 , find
∠ . Draw a picture!
5. Given ∆
with
if
10 and
≅
, and is the midpoint of
5. Draw a picture!
. Find the perimeter of ∆
,
6. The measures of two sides of a triangle are 3 and 4. Between what two numbers must the
measure of the third side fall?
7. Is it possible to draw a triangle those sides measure
a) 8, 9, 10?
b) 8, 9, 17?
c) 8, 9, 18?
8. In ∆
, ∠
70 and ∠
45 .
a) Is it true that
is the longest side of that triangle?
b) Write an extended inequality that compares the lengths of the sides of ∆
3,
9.
A
4. Find the length of the diagonal
B
X
D
C
10.
∠
30° . Find the measure of angle
.
.
.
11. State whether each statement is Always True, Sometimes True, or Never True.
a) A square is a rectangle.
b) If two of the angles of a trapezoid are congruent, then the trapezoid is isosceles.
c) The diagonals of a trapezoid bisect each other.
d) The diagonals of a parallelogram are perpendicular.
e) A rectangle is a square.
f) The diagonals of a square are perpendicular.
g) Two consecutive angles of a parallelogram are supplementary.
h) Opposite angles of a rhombus are congruent.
i) The diagonals of a rectangle are congruent.
j) The four sides of a kite a congruent.
k) The diagonals of a parallelogram bisect each other.
12. Which of the following principal(s) do NOT exist?
≅ ≅ ≅ ≅ ≅ ≅
13. Find the length of the median of a trapezoid if its upper base is 30 and the length of the
lower base is 6 more, than twice the length of the upper base.
14. In an isosceles triangle
,
∠ .
is an altitude. Find
A
CAD = (9x - 27)°
BAD = (3x - 3)°
C
15. In a rhombus
and ∠
.
with diagonals
M
A
P
H
T
B
D
and
,
∠
30° . Find
∠
16. Find the measures of the remaining angles of trapezoid
118 .
∠
63 and ∠
17. Complete the following proof:
Given: rectangle
with diagonals
≅
Prove:
M
N
Q
and
with
parallel to
, if
.
P
PROOF
Statements
1.
2.
Reasons
1.
is a parallelogram
2.
3.
3. Opposite sides of a parallelogram are
congruent
4.
4. Identity
5. ∠
and ∠
are right angles
5.
6.
6. All right angles are congruent
7.
7.
8.
8.
Math 1312 Popper 15
Popper 15 question 1: Consider rectangle MNPQ with diagonals MP and NQ. If NP = 8 and
MP = 12, find QP.
A. 2√5 B. 4√13 C. 4√5 D. 2√34 E. None of the above Popper 15 question 2: Consider rhombus ABCD with diagonals AC and DB. If AC = 10 and
DB = 4, find AD.
A. √14 B. √29 C. 2√26 D. √41 E. None of these Popper 15 question 3: Consider rhombus ABCD with diagonals AC and BD. Find measure of
angle ADC if measure of angle CAB = 15°.
A. 165° B. 75° C. 150° D. 30° E. None of the above Popper 15 question 4: Consider trapezoid ABCD with bases AB and DC. M and N are midpoints
of AD and BC, respectively. If MN = 40 and AB = 12, find CD.
A. 26 B. 40 C. 52 D. 68 E. None of these Popper 15 question 5: OP is the perpendicular bisector of MN . If MP = 5x + 2 and PN = 14 – x. Find MP. O M P N A. 12 B. 2 C. 10 D. 8 E. None of these Solutions to 13 and 14: Popper 13 question 1: Given a kite ABCD. AC is the perpendicular bisector of BD. Find BC if AB = 5 and the perimeter of the kite is 24. A D O B C A. 5 B. 7 C. 10 D 14 E. None of these Popper 13 question 2: In parallelogram ABCD (not shown), the diagonals have the lengths AC = 7 and BD = 9. Which pair of angles have greater measures? A A and D B. B and C C. A and C D. A and B E. None of these Use for Popper 13 questions 3‐5: HJKL is an isosceles trapezoid with bases HJ and LK , and median RS . Use the given information to solve each problem. L K
R S
J H Popper 13 question 3: If LK =30 and HJ = 42 then find RS. A. RS =36 B RS = 20 C. RS =7 D. RS =2 E. None of these Popper 13 question 4: If RS =17 and HJ = 14, find LK. A. LK =36 B LK = 20 C. LK =7 D. LK =2 E. None of these Popper 13 question 5: If RS = x + 5 and HJ + LK = 4x + 6 find RS. A. RS =36 B RS = 20 C. RS =7 D. RS =2 E. None of these Popper 14 question 1: State the method can be used to prove the triangles are congruent. ∆
≅∆
F D E G A. ASA B. SSS C. SAS D. AAS E. none of these Popper 14 question 2: What angle is the biggest? 1
M
O
8
6
N A. ∠ B. ∠ C. ∠ D. None of these Use for Popper 14 questions 3 and 4:Find the missing values. ∆ABE  ∆DBC. If AB = 2x +6, BD =20, CD = y + 7 and AE = 25 C
A
B
D E
Popper 14 question 3: Find the value of x. A. 20 B. 7 C. 14 D. none of these Popper 14 question 4: Find the value y. A. 18 B. 7 C. 15 D. None of these Popper 14 question 5: These triangles are congruent by HL. Find x if PQ =2x‐1 and DE = 41 P
D
F
E
Q
R A. 20 B. 21.5 C. 21 D. none of these A. 5 B. 7 C. 10 D 14 E. None of these