Geometry Honors

MIDTERM TOPICS FOR HONORS GEOMETRY

1. Logic

2. Midpoint

3. Distance

4. Slope

5. Perpendicular , Parallel Lines & Transversals

6. 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.

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.

10. Find the midpoint of the line segment with endpoints: Aand B .

11. Find y:

12. Find the measure of B.

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.

14. Given:

bisects ABC

m ABD = x + 5y

mDBC = 2x + 2y + 3

Find x and y.

15. The diagonals of a rhombus are 8 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 .

Geometry Honors – Midterm Review - Answers

1. Possible Answer

Given

Given

Law of Modus Tollens (1, 2)

(A B)

DeMorgan’s Law (3)

A B

Given

A

Law of Disjunctive Inference (4, 5)

B

Given

Law of Modus Tollens (7, 6)

D

Given

Law of Detachment (9, 8)

P

2. Possible Answer

Given

Law of Simplification (1)

B

Given

C

Law of Disjunctive Inference (3, 2)

Given

S

Law of Detachment (5, 4)

3. Given: ABC is isosceles with base

bisects

bisects

Prove: ADC is isosceles

Possible Answer

Definition of an Isosceles Triangle

Division Post.

Definition of angle bisector

Given

Definition of Isosceles Triangles

Given

4. Slope =

a = -3

b = 4

m =

5. Slope =

a = -4

b = 3

m =

y – y1 = m(x – x1)

y – 5 = (x – 1)

* Plug in 1 for y and solve for x.

1 – 5 = (x – 1)

-4 = (x – 1)

-3 = x – 1

-2 = x

6. a2 + b2 = c2a2 + b2 = c2

32 + 42 = c232 + 62 = c2

5 = c = RQ = PQ = c = RP = SP

Perimeter = 5 + 5 + + = 10 +

7. Yes! All angles are different and one angle is greater than 90.

8. Formula :

R = Midpoint of AB =( ) =(

H = Midpoint of CB =( ) =(

O = Midpoint of CD =( ) =(-

M = Midpoint of AB =( ) =(

RM =

OH =

OM =

HR =

OR=

HM =

9. 180 – x = 5(90 – x) – 30

180 – x = -5x + 420

x = 60

compl of angle = 30

of compl. = = 12

10.

MP =

MP =

MP =

MP =

11.

(x – 11) (x + 9) = 0

x = 11, x = -9

= (11)2 – 11 = 110

y + 110 + 40 = 180

y = 30

12. 10x – 45 = (2x + 10) + (4x + 5)

10x – 45 = 6x + 15

x = 15

m

13. Possible Answer

Formula:

PS=

LU =

PL =

SU =

SL=

UP =

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:

x = 15

y = 6

15.

4

4

4

4

8 = c

64 = c2

Perimeter = 4(8) = 32

(42 + 42 = c2

16.

Midpoint of AB = ( ) = (

CM =

CM=

CM=

CM= = =

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 and . 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.

7. Find m

M

8. Find m

9. E and F are midpoints, EF = 52.5 and DC = 32.5. Find AB

10. The consecutive sides of a rhombus are 14 –x and 2x + 5. Find the perimeter.

11.

Answer Key:

1. perpendicular

2. If I do not go to the gym, then I do not eat pizza.

3. Rectangle, parallelogram, square

4.

6

5.

2

6. x =5 and y =10

7. 51

8. 80

9. 72.5

10. 44

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