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Geometry Review

DescriptionGeometry CSA Review

Question #1If ΔABC and ΔXYZ are congruent, which of the following statements below is not true?

Angle B and angle Y are congruent.AAngle CBA and angle ZXY are congruent.BAB and XY are congruent.CAC and XZ are congruent.D

Question #2Given that ∠X ≅ ∠D, and DE ≅ XW, what is the third congruence needed to prove that ΔXWY ≅ΔDEC by ASA?

∠Y ≅ ∠CA

∠Y ≅ ∠EB

∠W ≅ ∠CC

∠W ≅ ∠ED

Question #3GEO 4.0 Angles

Use the figure to answer the following question(s).

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Given P||Q and T is a transversal, which of the following justifies ∠1 ≅ ∠5?

Corresponding Angles PostulateAAlternate Interior Angles TheoremBConsecutive Interior Angles TheoremCAlternate Exterior Angles TheoremD

Question #4Use the figure below to answer the following question:

Given that AD and BC bisect each other at E, which of the following justifies ΔABE ≅ ΔDCE?

SSS PostulateASAS PostulateBDefinition of Segment BisectorCDefinition of Congruent TrianglesD

Question #5

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Given:

Line segment WZ bisects line segment XYLine segment XY bisects line segment WZTo prove:

Triangles WAX and ZAY are congruent

Statement:

1. Segment WZ bisects XYReasons:

1. given

2. Segments XA and AY are

congruent

2. when a segment is bisected the resulting segments are

congruent

3. Segment XY bisects WZ 3. given

4. Angles WAX and YAZ are

congruent4. Opposite interior angles of intersecting lines are equal

5. Triangles WAX and ZAY are

congruent

5. Triangles with two sides and an included angle equal are

congruent

What should be in statement 4 to complete the proof?

Step 4 is not needed the proof works without it.ASegments WA and AZ are congruent.BSegments WX and YZ are congruent.CAngles WXA and ZYA are congruent.D

Question #6

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Triangle ABC is reflected over the line y = x to produce triangle A'B'C'.

What will be the coordinates of A'?

(2 , –1)A(–2 , –1)B(2 , 1)C(1 , 2)D

Question #7In the diagram below, AB and DE are parallel.

Which of the following statements must be true?

∠C is a right angleA∠D and ∠E are congruentBTriangles ABC and DEC are similar.CNone of the aboveD

Question #8Look at AB on the coordinate plane.

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Which coordinate plane shows AB after a 90 degree clockwise rotation about the origin?

A

B

C

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D

Question #9Which theorem or postulate can be used to prove ΔABD ≅ ΔCDB?

Given: AB||DC and AD||BC

AAAASABSSSCAASD

Question #10Define perpendicular lines.

Lines that cut across two or more lines.ATwo coplanar lines that do not intersect.BTwo coplanar lines that intersect at a 90 degree angle.CTwo non–coplanar lines that do not intersect.D

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Question #11In order to show that ΔFGH is congruent to ΔF'G'H', how many degrees must ΔFGH be rotatedclockwise about the origin?

90°A180°B270°C360°D

Question #12Examine ΔABC below.

Determine which of the following relationships are true.  Select all that apply.

DE = 2ACAm∠BCA = 2(m∠BED)BDE || ACC

Question #13

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Identify the triangles below that are similar by SAS similarity.

A

B

C

D

Question #14Based on the drawing below, in order for ΔABC to be similar to ΔDEF by SAS similarity, which ofthe following needs to be true?

m∠D = 38°Am∠D = 52°Bm∠F = 38°Cm∠F = 52°D

Question #15

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Hank writes a proof to show that vertical angles are congruent.

Given: Lines m and n intersect at a point.Prove: ∠1 ≅ ∠2

STATEMENTS REASONS1. Lines m and n intersect at a point Given

2. ∠1 and ∠3 are linear pairs ∠2 and ∠ 3 are linear pairs Definition of linear pairs

3. ∠1 and ∠3 are supplementaryangles∠2 and ∠3 are supplementary angles

Linear pairs are supplementary

4. Definition of supplementary angles

5. Substitution property

6. m∠1 = m∠2 Subtraction property

7. ∠1 ≅ ∠2 Definition of congruent angles

Part AWhich is the missing statement in step 4?

Part BWhich is the missing statement in step 5?

Question #16

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Mark is asked to prove that ∠4 ≅ ∠6, given that AB || CD, as shown in the diagram above.

Mark's proof is shown in the table below.

Step in Proof Statements1 ∠4 ≅ ∠8 therefore m∠4 = m∠8

2 ∠8 ≅ ∠6 therefore m∠8 = m∠6

3 If m∠4 = m∠8 and m∠8 = m∠6 then m∠4 =m∠6

4 ∠4 ≅ ∠6

Which reason supports the statement Mark made in step 2 of his work?

Vertical angles are congruent.ASupplementary angles are congruent.BCorresponding angles formed by parallel lines are congruent.CAlternate interior angles formed by parallel lines are congruent.D

Question #17Calculate the length of the side BC given the following data for 58°:

Sin 58° = 0.848Cos 58° = .530Tan 58° = 1.600

11.02A6.89B20.80C0.065D

Question #18

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Find the value of x.

16sin(35°)A16cos(35°)Bsin(35°)

16C

16sin(35°)

D

Question #19Use the figure below to answer the following question.

If AC||DE, which of the following justifies ΔABC ~ ΔDBE?

Definition of Similar TrianglesASAS Similarity TheoremBSSS Similarity TheoremCAA Similarity PostulateD

Question #20

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Marcus made a sail for his toy boat.  If the sail is 5 inches long and the top angle of the sail is 40°,what is the width of the bottom of the sail (w) to the nearest tens place?

3.2 inchesA3.9 inchesB4.2 inchesC5.0 inchesD

Question #21What is the approximate value of x in the figure below?

17.1A21.0B24.6C36.6D

Question #22

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Question #22Right triangle QRS is pictured below.

Which equation gives the correct value for RS?

cos 31 = 24.8RS

A

cos 31 = RS24.8

B

sin 31 = 24.8RS

C

sin 31 = RS24.8

D

Question #23The sun is behind a building and casting a shadow.  Approximately how long is the shadow if thebuilding is 25 feet tall and the angle of the shadow opposite the building is 27°? (Assume thebuilding is at a right angle to the ground.)

sin27° ≈ 0.45cos27° ≈ 0.89 tan27° ≈ 0.51

55.07 ft.A49.07 ft.B28.06 ft.C.02 ft.D

Question #24

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Find the volume of a sphere with a diameter of 22m. Round to the nearest tenth.

44,579.6 mA 3

5,572.4 mB 3

1,393.1 mC 3

506.6 mD 3

Question #25Find the volume of the cylinder.  Round the answer to the nearest hundredth.

324.59 ftA 3

216.97 ftB 3

435.20 ftC 3

681.64 ftD 3

Question #26

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This figure shows a pyramid with an altitude of 10 cm and an equilateral triangle base with sides 12cm long.

What is the volume of this equilateral pyramid?

A

B

C

D

Question #27A sphere has a radius r = 3 inches.  What is its approximate volume?

V = 43πr3

8π inA 3

12π inB 3

36π inC 3

108π inD 3

Question #28

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Find the volume of the cone and round to the nearest tenth.

490.1 in.A 3

545.3 in.B 3

1470.3 in.C 3

1960.4 in.D 3