## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

Prove that triangle ABC is congruent to triangle CDA if ABCD is a parallelogram.

## 2. | GCSE Higher |

The design below is made from six congruent trapezia and two red triangles.

Each trapezium has one line of symmetry.

The following statements were made about the red triangles:

- The red triangles are isosceles triangles.
- The red triangles are equilateral triangles.
- The red triangles are congruent triangles.

(a) Which statements must be true?

(b) Which statements could be true?

(c) Which statements must be false?

## 3. | GCSE Higher |

ABCD is a parallelogram with diagonals meeting at E. Prove that triangle ABE is congruent to triangle CDE.

## 4. | GCSE Higher |

ABC is an isosceles triangle in which AB = AC.

AD = AE.

Prove that triangle ABD is congruent to triangle ACE.

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