Problem solving with similarity | Starter Quiz | Oak National Academy

Which of these pairs of triangles are congruent?

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Answer explanation

The triangles in choice 1 are congruent by RHS as they both have a hypotenuse of 9 cm and a shorter side of 4 cm.

Pythagoras’ theorem states that the (a)   of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.

• 5 cm, 10 cm, 15 cm

• 5 cm, 12 cm, 13 cm

• 12 cm, 28 cm, 24 cm

• 20 cm, 24 cm, 26 cm

• 10 cm, 24 cm, 26 cm

A right-angled triangle has a hypotenuse of 65 mm. Select the possible lengths of the two shorter sides.

• 39 mm and 52 mm

• 20 mm and 35 mm

• 20 mm and 25 mm

• 16 mm and 63 mm

• 32 cm and 40 cm

Match each letter which the correct statement to complete the proof that triangle DAC and triangle ABC are congruent.

• a

• RHS

• b

• hypotenuse

• d

• ∠ABC

• c

• adjacent

Answer explanation

∠ADC = ∠ABC = 90° as they are given in the diagram. C is the hypotenuse of both triangles. DC = BC as they are adjacent sides on a kite. Hence, triangle DAC and triangle ABC are congruent by RHS.