Home › Worksheets › IGCSE Year 9 Math › Congruence and Similarity Prepared by Mohsim Digital Education
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AAA is not a congruence condition for triangles, and similar triangles keep equal angles with sides in one ratio, so this Year 9 sheet separates shapes that match exactly from shapes that only scale. The key also records a similarity ratio answer of 24 and an area ratio of 8 : 1.
Key Takeaways
AAA is not a valid congruence condition for triangles (Q1).
Similar triangles share equal angles and proportional sides (Q2).
The key records an area ratio of 8 : 1.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
Which of these is NOT a condition for two triangles to be congruent?
(a) SSS (b) SAS (c) AAA (d) RHS
2.
Similar triangles have corresponding sides in the same ratio and which other property?
(a) equal areas (b) equal angles (c) equal perimeters (d) equal heights
3.
A triangle with sides 3, 4 and 5 is enlarged by scale factor 2. What is the perimeter of the enlarged triangle?
(a) 12 (b) 6 (c) 24 (d) 48
4.
Two similar shapes have areas 25 cm² and 100 cm². What is the linear scale factor from the smaller to the larger?
(a) 4 (b) 5 (c) 0.5 (d) 2
5.
Two similar solids have side lengths in the ratio 2 : 1. What is the ratio of their volumes?
(a) 2 : 1 (b) 4 : 1 (c) 8 : 1 (d) 6 : 1
6.
Triangle ABC is congruent to triangle DEF. Which of the following must be true?
(a) Their perimeters are equal (b) Their angles are all 60 degrees (c) Their areas are different (d) They are mirror images
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
State what it means for two shapes to be congruent.
8.
Two similar triangles have scale factor 3. The smaller triangle has area 8 cm². Find the area of the larger triangle.
9.
A shape of perimeter 20 cm is enlarged by scale factor 2.5. Find the new perimeter.
10.
State in full what the RHS congruence condition stands for.
11.
A small rectangle is 4 cm by 6 cm. A similar larger rectangle is 8 cm wide. Find its length.
12.
Complete the sentence: similar figures have corresponding angles that are equal and corresponding sides that are proportional.
13.
A model car is built at scale 1 : 20. The real car is 4 m long. Find the length of the model in cm.
14.
Two similar cylinders have heights 6 cm and 9 cm. Give the ratio of their surface areas in simplest form.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
A flagpole casts a shadow 6 m long while a 1.5 m stick casts a shadow 1 m long. Find the height of the flagpole.
16.
Two similar triangles have areas 16 cm² and 36 cm². The smaller triangle has a base of 8 cm. Find the base of the larger triangle.
17.
A photograph measures 10 cm by 15 cm. It is enlarged so its width becomes 12 cm. Find the new length.
18.
Two similar cuboids have volumes 125 cm³ and 1000 cm³. Find the scale factor between them.
19.
A triangle with sides 5 cm, 6 cm and 7 cm is enlarged by scale factor 3. Give the ratio of the new area to the original area.
20.
A map has scale 1 : 50000. Two towns are 8 cm apart on the map. Find the real distance between them in km.
Answer Key
1. c) AAA
2. b) equal angles
3. c) 24
4. d) 2
5. c) 8 : 1
6. a) Their perimeters are equal
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
Which is NOT a congruence condition for triangles?
AAA, option (c) in this worksheet (Q1).
What do similar triangles have besides proportional sides?
Equal angles, option (b) in this worksheet (Q2).
What is the area ratio recorded in the key?
8 : 1.