Checking and securing understanding of congruent triangles (RHS) | Exit Quiz | Oak National Academy

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

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

• 6 cm, 8 cm, 10 cm

• 7 cm, 9 cm, 11 cm

• 9 cm, 12 cm, 15 cm

• 12 cm, 15 cm, 18 cm

• 15 cm, 20 cm, 25 cm

A right-angled triangle has a hypotenuse of 17 m. Select the possible lengths of the two shorter sides.

• 7 m and 14 m

• 8 m and 15 m

• 9 m and 13 m

• 10 m and 12 m

Which of these pairs of triangles are congruent?

• 
• 
• 
• 

Answer explanation

The triangles in choice 1 are congruent by RHS as they both have a hypotenuse of 20 cm and a shorter side of 9 cm. The hypotenuse in choice 4 is 5 as 4² + 3² = 5², so the triangles in choice 4 are also congruent.

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

• b

• 90°

• c

• RHS

• a

• AC

• d

• BC

Answer explanation

∠ADC = ∠ABC = 90° as they are given in the diagram. AC 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.