Geometry and proof · Ages 14–15

Parallel lines and similar triangles worksheet

Part of: Similar triangles

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Geometry and proof · Ages 14–15

Numsprite
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Name:Date:Score:／46

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.In the picture, DE // BC. x =
Answer:
2.In the picture, AB // DC, and AC and BD cross at E. x =
Answer:
3.In the picture, AB // DC, and AC and BD cross at E. x = , y =
Fill in each blank
Answer:
4.In the picture, DE // BC. x =
Answer:
5.In the picture, AB // DC, AC and BD cross at E, and EC is 4 cm longer than AE. x =
Answer:
6.In the picture, DE // BC. x =
Answer:
7.In the picture, AB // DC, AC and BD cross at E, and EC is 2 cm longer than AE. x =
Answer:
8.In the picture, AB // DC, AC and BD cross at E, and EC is 1 cm longer than AE. x =
Answer:
9.In the picture, AB // DC, AC and BD cross at E, and EC is 3 cm longer than AE. x =
Answer:
10.In the picture, AB // DC, AC and BD cross at E, and EC is 5 cm longer than AE. x =
Answer:

12.A street lamp is 4.5 m high. A person 2 m tall stands 7 m from the lamp post, and his shadow runs along the ground from his feet. How long is his shadow?
Working:
Answer:
13.To measure across a pond from A to B, pick a point E on the bank and carry AE on to C and BE on to D so that DC // AB. AE = 12 m, EC = 36 m and DC = 6 m. EC ÷ AE = , so AB = m.
Fill in each blank
Working:
Answer:
14.A tent's cross-section is a triangle ABC with the ground BC 8 m wide. A rope DE is tied to AB and AC parallel to the ground, with AD = 2 m and DB = 2 m. AB = m, and the rope DE = m.
Fill in each blank
Working:
Answer:
15.A stepladder's side view is shown: the bar DE is parallel to the ground BC, in dm (read the picture's cm as dm). AB = dm, DE = dm.
Fill in each blank
Working:
Answer:
16.To measure across a pond from A to B, pick a point E on the bank and carry AE on to C and BE on to D so that DC // AB. AE = 10 m, EC = 20 m and DC = 20 m. EC ÷ AE = , so AB = m.
Fill in each blank
Working:
Answer:
17.A tent's cross-section is a triangle ABC with the ground BC 6 m wide. A rope DE is tied to AB and AC parallel to the ground, with AD = 3 m and DB = 1 m. AB = m, and the rope DE = m.
Fill in each blank
Working:
Answer:

Show the answers and working

Parallel lines and similar triangles worksheet: Answers and working

1. 5 cm
△ADE ~ △ABC (AAA), and AB = 4 + 4 = 8 cm: x = 10 × 48 = 5.
2. 6 cm
△ABE ~ △CDE (AAA): CE ÷ AE = 6 ÷ 3 = 2, so x = 3 × 2 = 6 (corr. sides, ~△s).
3. 10, 12
△ABE ~ △CDE: the scale is DC ÷ AB = 12 ÷ 6 = 2; x goes with AE: 5 × 2 = 10; y goes with BE: 6 × 2 = 12.
4. 5 cm
ABAD = BCDE: AB = 5 × 10 ÷ 5 = 10 cm, so x = 10 − 5 = 5.
5. 6 cm
AECE = ABDC: xx + 4 = 35, so 5x = 3x + 3 × 4 and x = 6. Check: 6 : 10 = 3 : 5.
6. 2 cm
AEAC = ADAB, so AE : EC = AD : DB = 2 : 4: x = 4 × 2 ÷ 4 = 2.
7. 4 cm
AECE = ABDC: xx + 2 = 46, so 6x = 4x + 4 × 2 and x = 4. Check: 4 : 6 = 4 : 6.
8. 3 cm
AECE = ABDC: xx + 1 = 68, so 8x = 6x + 6 × 1 and x = 3. Check: 3 : 4 = 6 : 8.
9. 5 cm
AECE = ABDC: xx + 3 = 58, so 8x = 5x + 5 × 3 and x = 5. Check: 5 : 8 = 5 : 8.
10. 5 cm
AECE = ABDC: xx + 5 = 612, so 12x = 6x + 6 × 5 and x = 5. Check: 5 : 10 = 6 : 12.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

12. 5.6 m
The person and the post are parallel, so the two triangles are similar: ss + 7 = 24.5, so 4.5s = 2s + 2 × 7 and s = 5.6 m.
13. 3, 2
△ABE ~ △CDE (alt. ∠s, vert. opp. ∠s: AAA): scale = 36 ÷ 12 = 3, so AB = 6 ÷ 3 = 2 m.
14. 4, 4
AB = 2 + 2 = 4 m; DE // BC, so △ADE ~ △ABC: DE = 8 × 2 ÷ 4 = 4 m.
15. 12, 8
AB = 8 + 4 = 12; △ADE ~ △ABC, so DE = 12 × 8 ÷ 12 = 8 dm.
16. 2, 10
△ABE ~ △CDE (alt. ∠s, vert. opp. ∠s: AAA): scale = 20 ÷ 10 = 2, so AB = 20 ÷ 2 = 10 m.
17. 4, 4.5
AB = 3 + 1 = 4 m; DE // BC, so △ADE ~ △ABC: DE = 6 × 3 ÷ 4 = 4.5 m.

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