18.4 Congruence and congruence criteria — Practise with help
Attempt these from memory before opening the answers. Then try each question before opening a hint.
Warm-up: remember
Answer these from memory. Do not look back at the section.
- State the sum of the angles in a triangle.
- What does it mean for two lengths to be equal?
Check the warm-up
- .
- They have the same length.
If an answer differs, revisit Section 16.3 for triangle angle facts.
Practise with help
1. Two triangles have three matching side lengths. Name a criterion.
Hint
Count the matching sides.
Next step
Three sides correspond.
Full working
SSS proves the triangles congruent.
2. Two right triangles have equal hypotenuse and one equal shorter side.
Hint
Use the special criterion for right-angled triangles.
Next step
Both have a right angle, with matching hypotenuse and one leg.
Full working
RHS proves congruence.
3. Earlier topic: solve .
Hint
Use the inverse operation.
Next step
Divide both sides by .
Full working
.