Browse Congruence & similarity

44 questions at your level

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Congruent triangles & proof

16 questions

LessonNot started
ABCDABCD is a parallelogram. The diagonal ACAC is drawn.ABCDDiagram NOT accurately drawn

Prove that triangle ABCABC is congruent to triangle CDACDA.
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Here are four statements about two triangles.

A Two sides and the angle between them are equal.

B Two sides and an angle that is not between them are equal.

C All three angles are equal.

D A right angle, the hypotenuse and one other side are equal.

(a) Write down the letters of the two statements that prove the triangles are congruent.

(b) Explain why statement C does not prove the triangles are congruent.
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For each pair of triangles, write down the congruence condition (SSS, SAS, ASA or RHS) that proves they are congruent.

(a) All three pairs of corresponding sides are equal.

(b) Both triangles are right-angled, with equal hypotenuses and one other pair of equal sides.

(c) Two pairs of corresponding angles are equal, and the sides between those angles are equal.
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ABCDABCD is a parallelogram.ABCDDiagram NOT accurately drawn

Prove that triangle ABCABC is congruent to triangle CDACDA. (3 marks)
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In triangle ABCABC, AB=ACAB = AC. MM is the midpoint of BCBC.

(a) Prove that triangles ABMABM and ACMACM are congruent. [3]

(b) Hence explain why angle AMB=90°AMB = 90°. [1]
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Similar shapes & missing lengths

28 questions

LessonNot started
Triangle ABCABC and triangle PQRPQR are similar, with ABAB corresponding to PQPQ.8 cm7 cm20 cm30 cmABCPQRDiagram NOT accurately drawn

(a) Work out the length of QRQR.

(b) Work out the length of ACAC.
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Two similar tiles have corresponding sides of length 55 cm and 88 cm.

The smaller tile has an area of 4040 cm².

Work out the area of the larger tile.
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Two triangles are mathematically similar. A side of length 66 cm in the smaller triangle corresponds to a side of length 99 cm in the larger triangle.

(a) A second side of the smaller triangle is 88 cm. Work out the corresponding side of the larger triangle.

(b) A side of the larger triangle is 1515 cm. Work out the corresponding side of the smaller triangle.
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A vegetable plot is in the shape of a right-angled triangle ABCABC.ABCLena draws the vegetable plot to a scale of 11 cm to 66 m.

On the drawing, the vegetable plot has an area of 2727 cm²

In real life BC=54BC = 54 m.

Work out the real length of ABAB.

(3 marks)
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