Geometry and proof · Ages 14–15
The intercept theorem worksheet
Part of: Quadrilaterals
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The intercept theorem worksheet
Geometry and proof · Ages 14–15
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The three level lines in the picture are parallel. x =
Answer:
2.The four level lines in the picture are parallel. x =
Answer:
3.The three level lines in the picture are parallel, and DF = 16 cm. DE = cm, EF = cm
Fill in each blank
Answer:
4.Three parallel lines cut two lines at A, B, C and at D, E, F, with AB = BC, DE = (2x + 7) cm and EF = (4x − 11) cm. x =
Answer:
5.The three level lines in the picture are parallel, and DF = 10 cm. DE = cm, EF = cm
Fill in each blank
Answer:
6.Three parallel lines cut two lines at A, B, C and at D, E, F, with AB = BC, DE = (2x + 4) cm and EF = (5x − 20) cm. x =
Answer:
7.Four parallel lines cut two lines at A, B, C, D and at E, F, G, H, with AB = BC = CD, EF = (x + 2) cm and FG = (3x − 14) cm. GH =
Answer:
8.The four level lines in the picture are parallel, and EH = 24 cm. x =
Answer:
9.Four parallel lines cut two lines at A, B, C, D and at E, F, G, H, with AB = BC = CD, EF = (x + 1) cm and FG = (3x − 5) cm. GH =
Answer:
10.The four level lines in the picture are parallel, and EH = 12 cm. x =
Answer:
Part B: Choose, or true or false (2 marks each)
11.Three parallel lines cut two lines at A, B, C and at D, E, F. AB = 2 cm and BC = 5 cm, so DE = EF.
True or false?
Answer:
12.Three parallel lines cut two lines at A, B, C and at D, E, F. AB = 5 cm and BC = 5 cm, so DE = EF.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A ladder's rungs are parallel and evenly spaced along its left rail. The right rail is slanted, 135 cm from the lowest rung to the highest, cut into 5 pieces. Each piece on the right is cm; from the lowest rung to the third, the right rail is cm.
Fill in each blank
Working:
Answer:
14.A bookcase's shelves are parallel and evenly spaced along its left side. On the slanted right side, the stretch between shelves 1 and 2 is (x + 6) cm and between shelves 2 and 3 is (3x − 8) cm. How long is each stretch on the right?
Working:
Answer:
15.Four parallel streets cut two slanting roads. On the first road, the three stretches between neighbouring streets are each 147 m. The second road is 363 m from the first street to the fourth. Each stretch on the second road is m, and the first road is m in all.
Fill in each blank
Working:
Answer:
16.A sheet has parallel, evenly spaced ruled lines. A strip 10 cm long is laid slantwise with its ends on two lines, spanning 5 gaps. How long is each piece the lines cut it into?
Working:
Answer:
17.Four parallel streets cut two slanting roads. On the first road, the three stretches between neighbouring streets are each 131 m. The second road is 333 m from the first street to the fourth. Each stretch on the second road is m, and the first road is m in all.
Fill in each blank
Working:
Answer:
18.A ladder's rungs are parallel and evenly spaced along its left rail. The right rail is slanted, 130 cm from the lowest rung to the highest, cut into 5 pieces. Each piece on the right is cm; from the lowest rung to the third, the right rail is cm.
Fill in each blank
Working:
Answer:
Show the answers and working
The intercept theorem worksheet: Answers and working
Part A: Working out and filling in
1. 6 cm
AB = BC = 5 cm, so DE = EF (intercept thm.): x = 6.
2. 5 cm
AB = BC = CD = 5 cm, so EF = FG = GH (intercept thm.): x = 5.
3. 8, 8
AB = BC, so DE = EF (intercept thm.), each 16 ÷ 2 = 8 cm.
4. 9
AB = BC, so DE = EF (intercept thm.): 2x + 7 = 4x − 11, x = 9. Check: DE = EF = 25 cm.
5. 5, 5
AB = BC, so DE = EF (intercept thm.), each 10 ÷ 2 = 5 cm.
6. 8
AB = BC, so DE = EF (intercept thm.): 2x + 4 = 5x − 20, x = 8. Check: DE = EF = 20 cm.
7. 10 cm
EF = FG = GH (intercept thm.): x + 2 = 3x − 14, so x = 8 and GH = EF = 10 cm.
8. 8 cm
AB = BC = CD, so EF = FG = GH (intercept thm.): x = 24 ÷ 3 = 8.
9. 4 cm
EF = FG = GH (intercept thm.): x + 1 = 3x − 5, so x = 3 and GH = EF = 4 cm.
10. 4 cm
AB = BC = CD, so EF = FG = GH (intercept thm.): x = 12 ÷ 3 = 4.
Part B: Choose, or true or false
11. False
The intercept theorem needs AB = BC to give DE = EF; 2 cm and 5 cm must be equal.
12. True
The intercept theorem needs AB = BC to give DE = EF; 5 cm and 5 cm must be equal.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 27, 54
Equal pieces on the left mean equal pieces on the right (intercept thm.): 135 ÷ 5 = 27 cm; the lowest rung to the third is two pieces: 2 × 27 cm.
14. 13 cm
Even on the left means equal on the right (intercept thm.): x + 6 = 3x − 8, x = 7, each 13 cm.
15. 121, 441
Three equal stretches on the first road mean three equal ones on the second (intercept thm.): 363 ÷ 3 = 121 m; the first road is 3 × 147 = 441 m.
16. 2 cm
Evenly spaced parallels cut equal pieces off the strip too (intercept thm.): 10 ÷ 5 = 2 cm.
17. 111, 393
Three equal stretches on the first road mean three equal ones on the second (intercept thm.): 333 ÷ 3 = 111 m; the first road is 3 × 131 = 393 m.
18. 26, 52
Equal pieces on the left mean equal pieces on the right (intercept thm.): 130 ÷ 5 = 26 cm; the lowest rung to the third is two pieces: 2 × 26 cm.
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