Congruent triangles · Ages 13–14
Corresponding parts of congruent triangles
Match the letters in order: △ABC ≅ △PQR, AB = PQ, ∠C = ∠R.
How to do it
Method
Match the letters in order: △ABC ≅ △PQR, AB = PQ, ∠C = ∠R
△ABC ≅ △PQR, BC = 7 cm: QR = 7 cm (corr. sides, ≅△s)
Another way
By the picture: equal angles face matching sides
∠A = ∠P, so BC goes with QR
In full
Two triangles are congruent (written ≅) when one fits exactly on the other: corresponding sides are equal (reason: corr. sides, ≅△s), and corresponding angles are equal (reason: corr. ∠s, ≅△s). In △ABC ≅ △PQR the vertices are written in matching order: A goes with P, B with Q, C with R. One way: by the order of the letters. AB is the first and second letters, so it goes with the first and second of PQR: AB = PQ, and ∠C goes with ∠R. Another: by the picture. Sides facing equal angles correspond; the longest side faces the largest angle. Careful: a triangle may be turned round or flipped over in the picture, so don't go by where things are.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
In the picture, △ABC ≅ △QRP. x =
Show the answer and working
Answer: 5 cm
Match the letters in order: A with Q, B with R, C with P. The side marked x goes with the 5 cm side of △ABC (corr. sides, ≅△s).
Example 2
In the picture, △ABC ≅ △PQR. x =
Show the answer and working
Answer: 8 cm
Match the letters in order: A with P, B with Q, C with R. The side marked x goes with the 8 cm side of △ABC (corr. sides, ≅△s).
Example 3
The two triangles are congruent; sides with the same marks are equal. Which is written correctly?
- A. △ABC ≅ △PQR
- B. △ABC ≅ △PRQ
- C. △ABC ≅ △QPR
- D. △ABC ≅ △RQP
Choose the right answer
Show the answer and working
Answer: A. △ABC ≅ △PQR
Sides with the same marks correspond, and so do the vertices they face; in a ≅ statement, corresponding vertices go in the same places.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.In the picture, △ABC ≅ △QRP. x =
Answer:
2.In the picture, △ABC ≅ △PQR. x =
Answer:
3.The two triangles are congruent; sides with the same marks are equal. x = , y = .
Fill in each blank
Answer:
4.△ABC ≅ △PQR, ∠A = 56° and ∠B = 58°. Which is the largest angle of △PQR?
- A. ∠P
- B. All three are equal
- C. ∠R
- D. ∠Q
Choose the right answer
Answer:
5.△ABC ≅ △QRP, AB = 14 cm and RP = 6 cm, and the perimeter of △QRP is 31 cm. PQ =
Answer:
All the answers
- 1. 9 cm
- 2. 5 cm
- 3. 5, 6
- 4. C. ∠R
- 5. 11 cm
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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