Angle rules including parallel lines, interior and exterior angles of polygons, congruence and similarity, and the circle theorems needed at Higher tier.
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1.What do angles on a straight line add up to?
180 degrees.
2.What do angles around a point add up to?
360 degrees.
3.What is true of vertically opposite angles?
They are equal.
4.What are corresponding angles?
Angles in matching positions where a line crosses two parallel lines. They are equal, and form an F shape.
5.What are alternate angles?
Angles on opposite sides of a line crossing two parallel lines. They are equal, and form a Z shape.
6.What are co-interior angles?
Angles on the same side between two parallel lines. They add up to 180 degrees, and form a C shape.
7.What do the angles in a triangle add up to?
180 degrees.
8.What do the angles in a quadrilateral add up to?
360 degrees.
9.State the formula for the sum of the interior angles of a polygon.
sum = (number of sides minus 2) x 180
10.Find the interior angle sum of a hexagon.
(6 minus 2) x 180 = 720 degrees.
11.What do the exterior angles of any polygon add up to?
360 degrees.
12.How do you find one exterior angle of a regular polygon?
360 divided by the number of sides.
13.Find one interior angle of a regular pentagon.
Exterior angle = 360 divided by 5 = 72, so interior = 180 minus 72 = 108 degrees.
14.What is an isosceles triangle?
One with two equal sides and two equal base angles.
15.What is an equilateral triangle?
One with three equal sides and three angles of 60 degrees.
16.What does congruent mean?
Exactly the same shape and size, though possibly rotated or reflected.
17.State the four conditions for congruent triangles.
Side side side, side angle side, angle side angle, and right angle hypotenuse side.
18.What does similar mean?
The same shape but a different size, so corresponding angles are equal and corresponding sides are in the same ratio.
19.How do you find a missing side in similar shapes?
Find the scale factor by dividing a known pair of corresponding sides, then multiply or divide.
20.What is the angle in a semicircle?
90 degrees, where the triangle is drawn from the ends of a diameter.
21.What is the relationship between the angle at the centre and at the circumference?
The angle at the centre is twice the angle at the circumference, when both are subtended by the same arc.
22.What is true of angles in the same segment?
They are equal.
23.What is true of opposite angles in a cyclic quadrilateral?
They add up to 180 degrees.
24.What is the angle between a tangent and a radius?
90 degrees, at the point where the tangent touches the circle.
25.What does the alternate segment theorem say?
The angle between a tangent and a chord equals the angle in the alternate segment.
26.What is true of two tangents drawn from the same point?
They are equal in length.
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