Mathematics 1: Geometry and Measures

What is the sum of angles around a point?

360°

What is the sum of angles on a straight line?

180°

What are vertically opposite angles?

Opposite angles formed by intersecting lines; they are equal.

What is the sum of the interior angles of a triangle?

180°

What is the sum of the exterior angles of any polygon?

360°

What is the formula for the sum of the interior angles of an n-sided polygon?

(n−2)×180°

What is a regular polygon?

A polygon with all sides and all angles equal.

What conditions are sufficient to prove two triangles are congruent?

SSS, SAS, ASA or RHS.

What does it mean for two shapes to be similar?

They have the same shape but may have different sizes; corresponding angles are equal and sides are in proportion.

If the scale factor is k, how do areas scale?

By k².

If the scale factor is k, how do volumes scale?

By k³.

State Pythagoras' theorem.

a²+b²=c² for a right-angled triangle.

When can Pythagoras' theorem be used?

Only for right-angled triangles.

What is the circumference of a circle?

2πr or πd.

What is the area of a circle?

πr².

What is the volume of a cylinder?

πr²h.

What is an arc?

A portion of a circle's circumference.

What is a sector?

A region enclosed by two radii and an arc.

How do you find the length of an arc?

(θ/360)×2πr.

How do you find the area of a sector?

(θ/360)×πr².

What is a tangent to a circle?

A line that touches the circle at exactly one point.

What is the angle between a radius and a tangent?

90°.

What are the three trigonometric ratios?

sinθ=opposite/hypotenuse, cosθ=adjacent/hypotenuse, tanθ=opposite/adjacent.

What is sin 30°?

1/2.

What is cos 60°?

1/2.

What are the exact values of sin 45° and cos 45°?

√2/2.

What is tan 45°?

1.

What is tan 60°?

√3.

How do you calculate the area of a triangle?

1/2 × base × perpendicular height.

How do you calculate the area of a trapezium?

1/2 × (sum of parallel sides) × height.

How do you calculate the volume of a prism?

Cross-sectional area × length.

What is a three-figure bearing measured from?

North, measured clockwise.

What is a vector?

A quantity with both magnitude and direction.

How do you add vectors?

Add corresponding components.

What is the difference between a scalar and a vector?

A scalar has magnitude only; a vector has magnitude and direction.

What is a common ESAT geometry mistake?

Using Pythagoras or SOHCAHTOA on a triangle that is not right-angled.