Congruent Triangles
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Either paper 1 markShapes A, B, C and D are drawn on a square grid. Shape A Shape B Shape C Shape D Which two shapes are congruent? Circle your answer.
B and A C and D B and C D and A -
Either paper 1 mark
Here are two triangles.
The triangles are congruent. Circle the reason why these triangles are congruent.
ASA RHS SAS SSS
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Either paper 1 mark
Here are four triangles, A, B, C and D. The diagrams are not drawn accurately.
Triangle A
Triangle B
Triangle C
Triangle D
Which two triangles are congruent? Give the two letters.
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Either paper 3 marks
This shape is made from two triangles and four parallelograms with the same acute angle. The two parallelograms in each row are congruent to each other, but the top row need not be the same size as the bottom row. The shape has two rows, one above the other. Each row is a parallelogram, a triangle and a parallelogram side by side. The diagram shows one row and is not drawn accurately.
The acute angle of each parallelogram is between 36° and 40°.
For each statement, tick the correct box: must be true, could be true or must be false.
(a)The angle between the two sloping sides of a triangle is larger than each of its other two angles.
(b)The triangles are equilateral.
(c)The triangles are right-angled.
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Either paper 3 marks
\(ABCD\) is a quadrilateral. The diagonal \(AC\) has been drawn.
\(AB = AD\), as the dashes show, and \(CB = CD\).
(a)Using only the information given, write down the condition (SSS, SAS, ASA or RHS) that shows triangle \(ABC\) and triangle \(ADC\) are congruent.
(b)Hence write down the angle that must be equal to angle \(BAC\).
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Either paper 2 marks
Triangle \(ABC\) and triangle \(PQR\) are congruent, with \(A\) matching \(P\), \(B\) matching \(Q\) and \(C\) matching \(R\).
\(AB = PQ\), \(AC = PR\) and \(\angle BAC = \angle QPR\).
In triangle \(ABC\), \(AB = 21\) cm, \(BC = 20\) cm and \(AC = 29\) cm.
(a)Write down the condition (SSS, SAS, ASA or RHS) that the three facts above show.
(b)Write down the length of \(PR\).
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Either paper 3 marks
\(ABC\) is a triangle with \(AB = AC = 13\) cm and \(BC = 12\) cm.
The dashed line runs from \(A\) to the point \(M\) on \(BC\), and \(AM\) is perpendicular to \(BC\).
(a)Using only the information given, write down the condition (SSS, SAS, ASA or RHS) that shows triangle \(ABM\) and triangle \(ACM\) are congruent.
(b)Hence state the length of \(BM\).
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Either paper 2 marks
Triangle \(ABC\) has \(AB = 14\) cm, \(BC = 15\) cm and \(\angle BCA = 62^\circ\).
Triangle \(PQR\) has \(PQ = 14\) cm, \(QR = 15\) cm and \(\angle QRP = 62^\circ\).
Are the two triangles necessarily congruent?
Write Yes or No, and give a reason for your answer.
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Either paper 3 marks
\(ABCD\) is a parallelogram with \(AB = 14\) cm and \(BC = 6\) cm. The diagonal \(AC\) has been drawn.
Angle \(ABC = 78^\circ\).
(a)Write down the condition (SSS, SAS, ASA or RHS) that shows triangle \(ABC\) and triangle \(CDA\) are congruent.
(b)State the size of angle \(CDA\).
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Either paper 2 marks
In triangle \(ABC\), angle \(ABC = 48^\circ\), angle \(BCA = 69^\circ\) and \(BC = 7\) cm.
In triangle \(PQR\), angle \(PQR = 48^\circ\), angle \(QRP = 69^\circ\) and \(QR = 7\) cm.
Are the two triangles congruent, similar but not congruent, or neither?
You must give a reason for your answer.
- D and A
- RHS
- A and C
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(a) Must be true
(b) Must be false
(c) Must be false -
(a) SSS
(b) \(\angle DAC\) -
(a) SAS
(b) \(29\ \text{cm}\) -
(a) RHS
(b) \(6\ \text{cm}\) - No, because the angle given does not lie between the two sides given, and two different triangles can be drawn from that information
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(a) SSS
(b) \(78^\circ\) - congruent, because two pairs of angles are equal and so are the sides between them, which is ASA
Takes a couple of seconds the first time a sheet is made.