Common Core HSG.SRT.B.5 worksheet

Question 1

Triangles PQR and XYZ have PQ = XY and QR = YZ. Which extra fact would prove them congruent by SAS?

• A. RP = YZ
• B. ∠Q = ∠Y
• C. ∠R = ∠Z
• D. ∠P = ∠X

Question 2

Triangles ABC and DEF are similar. AB = 7 cm, BC = 9 cm and DE = 14 cm. Find EF in cm.

Answer 

Question 3

Aisha is 1.2 m tall and casts a 1.2 m shadow. At the same moment a tree casts a 21 m shadow. How tall is the tree, to 1 decimal place?

Answer 

Question 4

Two similar solids have a length scale factor of 3. The smaller has volume 18 cm³. What is the volume of the larger, in cm³?

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Question 5

Two triangles are known to be congruent because all three pairs of sides are equal. Which condition is this?

• A. SSS
• B. SAS
• C. RHS (HL)
• D. ASA

Question 6

Two triangles have two angles and the included side equal (ASA). Must they be congruent?

• A. Yes
• B. No

Question 7

Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 4 cm, PQ = 12 cm and BC = 7 cm. Find QR.

Answer 

Question 8

In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 2 cm, DB = 4 cm and DE = 5 cm. Find BC.

Answer 

Question 9

Triangles ABC and DEF have: ∠A = ∠D, ∠B = ∠E, BC = EF. Which test proves they are congruent?

• A. SAS
• B. AAS
• C. RHS (hypotenuse–leg)
• D. SSS

Question 10

Triangles PQR and XYZ have PQ = XY and QR = YZ. Which extra fact would prove them congruent by SAS?

• A. ∠Q = ∠Y
• B. ∠P = ∠X
• C. ∠R = ∠Z
• D. RP = YZ

Question 11

Triangles ABC and DEF are similar. AB = 10 cm, BC = 9 cm and DE = 25 cm. Find EF in cm.

Answer 

Question 12

Ben is 1.5 m tall and casts a 2 m shadow. At the same moment a tree casts a 16 m shadow. How tall is the tree, to 1 decimal place?

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Question 13

Two similar shapes have a length scale factor of 3. The smaller has area 15 cm². What is the area of the larger, in cm²?

Answer 

Question 14

Two triangles are known to be congruent because two angles and the side between them are equal. Which condition is this?

• A. SAS
• B. ASA
• C. RHS (HL)
• D. SSS

Question 15

Two triangles have only two pairs of sides equal. Must they be congruent?

• A. Yes
• B. No

Question 16

Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 10 cm, PQ = 40 cm and BC = 6 cm. Find QR.

Answer