MIDTERM TOPICS FOR HONORS GEOMETRY
1.
2.
3.
4.
5.
6.
Logic
Midpoint
Distance
Slope
Perpendicular , Parallel Lines & Transversals
Special Segments of Triangles (Angle bisector, Segment bisector, medians, and
altitudes)
7. Triangle Properties (interior angles, exterior angle theorem, etc..)
8. Proving Triangle Congruence / CPCTC
9. Properties of Parallelograms
10.Properties of Special Parallelograms
11.Trapezoids
12. Quadrilateral Proof
13. Coordinate Geometry (Midpoint, Distance, Slope, and Equations of Lines)
14. Coordinate Proof
15. Analytic Geometry
16. Midsegments of Trapezoids
Name____________________________________ Ms.Williams/Mrs. Hertel/Mr. Lambert
Geometry Honors 2015 - Midterm Review A
1. Write a formal proof:
Given:
D→ B
~D → P
(A  B) → C
~C
A
Prove: P
2. Given: A  ~ B
BC
C→S
Prove: S
3. Write a formal proof:
If a triangle is isosceles, the triangle formed by its base and the angle bisectors of its base angles is also
isosceles.
4. What is the slope of a line perpendicular to the line 4y -3x = 7?
5. A line is parallel to the line 3y - 4x = 7. It contains the point (1, 5) and has a point that has a y coordinate of
1. Find the x coordinate.
6. Find the perimeter of PQRS if ABCD is a rectangle.
Q
7. Can a triangle be obtuse and scalene?
8. Given ABCD with coordinates A(0,0), B(3,4), C(0,8) and D(-3,4). Quadrilateral RHOM is formed from the
midpoints of AB, BC, CD, and AD, respectively. Give the most descriptive name for quadrilateral RHOM and
explain why.
10
8
6
4
2
-10 -8 -6 -4 -2
2
4
6
8 10
-2
-4
-6
-8
-10
9. The measure of the supplement of an angle is 30 less than five times the measure of the complement. Find
two-fifths the measure of the complement.
 1 2 3 6  2 
 and B
10. Find the midpoint of the line segment with endpoints: A 
,
3 
 2
11. Find y:
y 99
2
40 x - x
x
12. Find the measure of ∡B.
A
4x + 5
2x + 10
B
10x - 45
C
 2  3 3 2 2 


 3 , 2 .


13. Prove that the quadrilateral with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a
rectangle but not a square.
A
14. Given:
̅̅̅̅  𝐵𝐶
̅̅̅̅
𝐴𝐵
̅̅̅̅
𝐵𝐷 bisects ∡ABC
m∡ ABD = x + 5y
m∡DBC = 2x + 2y + 3
D
B
Find x and y.
C
15. The diagonals of a rhombus are 8 3 and 8. Find the perimeter of the rhombus.
16. Given ABC, with coordinates A(0,2), B(7,4) and C(5, 0).
̅̅̅̅ .
Find the length of the median to 𝐴𝐵
Geometry Honors – Midterm Review - Answers
1. Possible Answer
Given
Given
 (A  B)
Law of Modus Tollens (1, 2)
 A  B
DeMorgan’s Law (3)
A
Given
B
Law of Disjunctive Inference (4, 5)
Given
D
Law of Modus Tollens (7, 6)
Given
P
Law of Detachment (9, 8)
2. Possible Answer
Given
B
Law of Simplification (1)
Given
C
Law of Disjunctive Inference (3, 2)
Given
S
Law of Detachment (5, 4)
3.
̅̅̅̅
Given: ABC is isosceles with base 𝐴𝐶
̅̅̅̅
𝐴𝐷 bisects ∡𝐴
̅̅̅̅
𝐶𝐷 bisects ∡𝐶
Prove: ADC is isosceles
Possible Answer
Given
̅̅̅̅
̅̅̅̅
𝐴𝐵 ≅ 𝐶𝐵
Definition of Isosceles Triangles
∡𝐴 ≅ ∡𝐶
Given
∡𝐷𝐴𝐶 ≅ ½ ∡𝐴
∡𝐷𝐶𝐴 ≅ ½ ∡𝐶
∡𝐷𝐴𝐶 ≅ ∡𝐷𝐶𝐴
Definition of angle bisector
Division Post.
̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐶𝐷
Definition of an Isosceles Triangle
4. Slope =
−𝑎
𝑏
a = -3
b=4
m
=
𝑏
𝑎
=
4
−3
5. Slope =
−𝑎
𝑏
a = -4
b=3
m=
4
3
y – y1 = m(x – x1)
4
y – 5 = (x – 1)
3
* Plug in 1 for y and solve for x.
1–5=
-4 =
4
3
4
(x – 1)
3
(x – 1)
-3 = x – 1

-2 = x
6. a2 + b2 = c2
a2 + b2 = c2
32 + 42 = c2
32 + 62 = c2
5 = c = RQ = PQ
3√5 = c = RP = SP
Perimeter = 5 + 5 + 𝟑√𝟓 + 𝟑√𝟓 = 10 + 𝟔√𝟓
7. Yes! All angles are different and one angle is greater than 90.
8. Formula :
d  (x) 2  (y ) 2
R = Midpoint of AB =(
H = Midpoint of CB =(
O = Midpoint of CD =(
M = Midpoint of AB =(
0+3 0+4
,
2
2
2
0+3 8+4
,
2
2
3
) =( , 2)
3
) =( , 6)
2
0+ −3 8+4
2
,
2
0+ −3 0+4
2
,
2
3
) =(- , 6)
2
3
) =( − , 2)
2
RM = √(3)2 + (0)2 = √9
OH = √(3)2 + (0)2 = √9
̅̅̅̅̅ ≅ ̅̅̅̅
𝑅𝑀
𝑂𝐻
OM = √(0)2 + (4)2 = √16
HR = √(0)2 + (4)2 = √16
̅̅̅̅̅ ≅ 𝐻𝑅
̅̅̅̅
𝑂𝑀
𝑅𝐻𝑂𝑀 𝑖𝑠 𝑎 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚
OR= √(−3)2 + (4)2 = √25
HM = √(3)2 + (4)2 = √25
̅̅̅̅ ≅ ̅̅̅̅̅
𝑂𝑅
𝐻𝑀
𝑅𝐻𝑂𝑀 𝑖𝑠 𝑎 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑖𝑡 𝑖𝑠 𝑎 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 𝑤𝑖𝑡ℎ 𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠.
9. 180 – x = 5(90 – x) – 30
180 – x = -5x + 420
x = 60
compl of angle = 30
2
5
of compl. =
2
∙ 30 = 12
5
10.
1 1+2√3
2
2
MP = [
+
2+√3
3
1 3+ 6√3 + 4 + 2√3
MP = [
2
6
1 7+ 8√3
MP = [
2
6
,
6−√2
,
3
+
7+ 8√3
12
,
6
21 + 4√2
6
21 + 4√2
12
]
12− 2√2 + 9 + 6√2
,
]

MP = [
3+2√2
2
]
11. 𝑥 2 − 𝑥 = 𝑥 + 99
𝑥 2 − 2𝑥 − 99 = 0
(x – 11) (x + 9) = 0
x = 11, x = -9
𝑥 2 − 𝑥 = (11)2 – 11 = 110
y + 110 + 40 = 180

y = 30
]
12.
10x – 45 = (2x + 10) + (4x + 5)
10x – 45 = 6x + 15
x = 15
m∡𝐵 = 2(15) + 10 = 40
13. Possible Answer
Formula: d  (x) 2  (y ) 2
PS= √(−1)2 + (2)2 = √5
LU = √(−1)2 + (2)2 = √5
̅̅̅̅ ≅ ̅̅̅̅
𝑃𝑆
𝐿𝑈
PL = √(4)2 + (2)2 = √20
SU = √(4)2 + (2)2 = √20
̅̅̅̅
̅̅̅̅ ≅ 𝑆𝑈
𝑃𝐿
𝑃𝐿𝑈𝑆 𝑖𝑠 𝑎 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚
SL= √(5)2 + (0)2 = √25
UP = √(3)2 + (4)2 = √25
̅̅̅ ≅ 𝑈𝑃
̅̅̅̅
𝑆𝐿
𝑃𝐿𝑈𝑆 𝑖𝑠 𝑎 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑖𝑡 𝑖𝑠 𝑎 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 𝑤𝑖𝑡ℎ 𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠.
It is not a square b/c all 4 sides are not congruent.
14.
Equation 1: x + 5y + 2x + 2y + 3 =90
3x + 7y = 87
Equation 2: x + 5y = 2x + 2y + 3
-x + 3y = 3
System: {
3x + 7y = 87
}
−x + 3y = 3
 x = 15
y=6
15.
(4√𝟑)2 + 42 = c2
4
64 = c2
4√𝟑
8= c
Perimeter = 4(8) = 32
16.
Midpoint of AB = (
0+7 2+4
2
,
3 2
CM = √( ) + (3)2
2
9
CM= √ + 9
4
9
36
4
4
CM= √ +
CM= √
45
4
=
√45
√4
=
3 √5
2
2
)=(
7
2
, 3)
4√𝟑
4
Geometry Honors 2015
Midterm Review #B
1. If line m is parallel to line p and ED is perpendicular to m, is ED parallel to or perpendicular to p?
2. Write the contrapositive of “ If I eat pizza then I go to the gym.”
3. Name the quadrilateral;
a. Diagonals are congruent but not perpendicular.
b. Diagonals bisect each other and are not congruent.
c. Diagonals are congruent and perpendicular.
4. The diagonals of a rhombus are 2 7 and 5 5 . Find the perimeter of the rhombus.
5. Find the distance between the points D(h-t, b + s) and E(h + t, b – s)
6. Find the value of x and y.
10x + 4y 26x - 4y
90
7. Find m<M
84
151 - 2y
6y + 3
M
8. Find m <TUD
F
T
B
6x + 10
4x + 20
A
U
C
E
D
9. E and F are midpoints, EF = 52.5 and DC = 32.5. Find AB
B
A
E
F
D
C
10. The consecutive sides of a rhombus are 14 –x and 2x + 5. Find the perimeter.
11.
Answer Key:
1.
2.
3.
4.
perpendicular
If I do not go to the gym, then I do not eat pizza.
Rectangle, parallelogram, square
6 17
5. 2 t 2  s 2
6. x =5 and y =10
7. 51
8. 80
9. 72.5
10. 44
11.