Geometry Practice Test

Find the coordinates of the midpoint of the segment whose endpoints are H(3, 7) and K(7, 1).

(5,4)

Write a rule to describe the transformation that is a reflection over the y-axis.

(x,y) > (-x,y)

Write a rule to describe the transformation that is a reflection over the x-axis.

(x,y) > (x,-y)

Name an angle supplementary to ∠COD.

angle COA

∠DFG and ∠JKL are complementary angles. m∠DFG = x + 8, and m∠JKL = x − 10. Find the measure of each angle.

angle DFG = 54; angle JKL = 36

Given: m∠PQR = x + 1, m∠SQR = x + 3, and m∠PQS = 100. Find x. m∠PQR + m∠SQR = m∠PQS a. _____ x + 1 + x + 3 = 100 b. Substitution Property 2x + 4 = 100 c. Simplify 2x = 96 d. _____ x = 48 e. Division Property of Equality

angle addition postulate; subtraction property of equality

Name a median for ΔABC.

line segment DB or BD

Is the statement a good definition? If not, find a counterexample. A square is a figure with two pairs of parallel sides and four right angles.

no; a rectangle is a counterexample.

Supplementary angles are two angles whose measures have sum ____. Complementary angles are two angles whose measures have sum ____.

180;90

ABCD is a parallelogram. If m∠CDA = 66, then m∠BCD = ? . The diagram is not to scale.

114 degrees

Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square.

4 blocks shorter

Solve the proportion. 3y − 8/ 12 = y/ 5

40/3

Find the length of the midsegment. The diagram is not to scale.

42

Solve for x.

5

ΔQRS ∼ ΔTUV. What is the measure of ∠V?

70 degrees

What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units?

71 degrees

Use the information in the diagram to determine the height of the tree. The diagram is not to scale.

75 feet

SQ ⎯⎯→ bisects ∠RST, and m∠RSQ = 4x − 5. Write an expression for ∠RST. The diagram is not to scale.

8x - 10

Given: PQ is parallel to BC. Find the length of AQ. The diagram is not drawn to scale.

9

Which two lines are parallel? I. 5y = −3x − 5 II. 5y = −1 − 3x III. 3y − 2x = −1 A. I and II B. I and III C. II and III D. No two of the lines are parallel.

A. I and II

How are the two angles related? A. Supplementary B. Vertical C. Complementary D. Adjacent

A. Supplementary

Explain why the triangles are similar. Then find the value of x

AA postulate; 4 2/3 or 14/3

Triangles ABC and DEF are similar. Find the lengths of AB and EF. DIAGRAM

AB = 10; EF = 2

Points B, D, and F are midpoints of the sides of ΔACE. EC = 30 and DF = 23. Find AC. The diagram is not to scale.

AC = 46

The two rectangles are similar. Which is a correct proportion for corresponding sides? A. 12 /8 = x/ 4 B. 12 /4 = x/ 8 C. 12 /4 = x/ 20 D. 4 /12 = x /8

B. 12 /4 = x/ 8

In ΔABC, G is the centroid and BE = 9. Find BG and GE.

BG = 3; GE = 6

Complete the statement. If a transversal intersects two parallel lines, then angles are supplementary. a. acute B. alternate interior C. same-side interior D. corresponding

C. Same-side interior

Give the slope-intercept form of the equation of the line that is perpendicular to 7x + 3y = 18 and contains P(6, 8). A. y - 6 = 3 7 (x - 8) B. y = 3 7 x + 18 /7 C. y = 3 7 x + 38 /7 D. y - 8 = 3 7 (x - 6)

C. y = 3 7 x + 38 /7

Which biconditional is NOT a good definition? A. A whole number is odd if and only if the number is not divisible by 2. B. An angle is straight if and only if its measure is 180. C. A whole number is even if and only if it is divisible by 2. D. A ray is a bisector of an angle if and only if it splits the angle into two angles.

D. A ray is a bisector of an angle if and only if it splits the angle into two angles.

Write an equation for the line perpendicular to y = 2x - 5 that contains (-9, 6). A. y - 6 = 2(x + 9) B. x - 6 = 2(y + 9) C. y - 9 = − 1 2 (x + 6) D. y - 6 = − 1 2 (x + 9)

D. y - 6 = − 1 2 (x + 9)

M is the midpoint of CF for the points C(3, 4) and F(9, 8). Find MF.

MF = SQUARE ROOT OF 13

Supply the reasons missing from the proof shown below. Given: AB ≅ AC, ∠BAD ≅ ∠CAD Prove: AD bisects BC Statements Reasons 1. AB ≅ AC 1. Given 2. ∠BAD ≅ ∠CAD 2. Given 3. AD ≅ AD 3. Reflexive Property 4. ΔBAD ≅ ΔCAD 4. ? 5. BD ≅ CD 5. ? 6. AD bisects BC 6. Def. of segment bisector

SAS; CPCTC

Justify the last two steps of the proof. Given: RS ≅ UT and RT ≅ US Prove: ΔRST ≅ ΔUTS Proof: 1. RS ≅ UT 1. Given 2. RT ≅ US 2. Given 3. ST ≅ TS 3. ? 4. ΔRST ≅ ΔUTS 4. ?

Symmetric Property of congruence; SSS

Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.

Yes; opposite angles are congruent.

Which overlapping triangles are congruent by AAS?

triangle ADC is congruent to triangle EBC

Write a similarity statement for the triangles. DIAGRAM

triangle CDE is similar to FGH

The polygons are similar, but not necessarily drawn to scale. Find the values of x and y. (hint use scale factor and then set cross factors equal to one another)

x = 9; y = 27

Find the values of the variables in the parallelogram. The diagram is not to scale.

x=29; y=49; z=102

Find the values of x and y

x=90; y=43

Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

yes; triangle ACB is congruent to triangle ACD