Geometric reasoning and proof

A, C and D are points on a circle, diameter AC. ABC is an isosceles triangle with AC = BC BCD is a straight line.

Work out the size of angle x.

AB and CD are straight, parallel lines. P is a point on AB. Q is a point on CD. AP = AQ

Work out the value of x.

In the diagram, ABCD and AEFG are congruent rectangles

Prove that GD bisects angle ADF.

ABCD is a trapezium. All four sides are different lengths. AB is parallel to CD. The diagonals intersect at X.

For each statement, tick the correct box.

In this isosceles triangle, AB = AC

The perimeter of the triangle is 22 cm Work out the length of AB.

AB, BC and CD are sides of a regular 12-sided polygon. CDMN is a square.

Prove that points A, B and N lie on a straight line.

A, B and C are three points on a circle. The radii from A, B and C are shown.

Is AC a diameter of the circle? You must show your working.

A, B and C are three points on a circle. The radii from A, B and C are shown.

Is AC a diameter of the circle? You must show your working.

In rectangle ABCD triangle ABE is equilateral triangle CDE is isosceles, with CE = DE

Work out the size of angle x.

Trapezium ABCE is made from parallelogram ABCD and isosceles triangle ADE.

Work out the size of angle AED.

The diagram shows a triangle and a trapezium.

Prove that a = b