Year 10 in England

9th grade geometry

4 9th grade geometry skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.

Mixed review

Ten questions drawn from every skill below.

Print a review worksheet Riddle puzzle on screen Bingo

Similar shapes

CCSS 8.G.A.4CCSS HSG.SRT.A.2CCSS HSG.SRT.B.5England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Example

Triangles ABC and DEF are similar. AB = 3 cm, BC = 8 cm and DE = 9 cm. Find EF in cm.

k = 9 ÷ 3 = 3
EF = 8 × 3 = 24 cm

Answer: 24

Builds on: Scale factors and enlargement, Proportional relationships

Leads to: Trigonometric ratios: SOH CAH TOA, Decide whether two triangles are similar, Find missing lengths in similar triangles

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Arc length and sector area

CCSS HSG.C.B.5England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Example

A sector has radius 11 cm and angle 30°. Find the arc length in cm, rounded to 1 decimal place.

(30/360) × 2 × π × 11
≈ 5.8 cm

Answer: 5.8

Builds on: Area of a circle

Leads to: The unit circle and radians, Find the angle or radius from an arc length or sector area, Find the perimeter of a sector, Arc length and sector area in radians

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Congruent triangles

CCSS HSG.CO.B.8CCSS HSG.SRT.B.5England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Example

Two triangles are known to be congruent because two sides and the angle between them are equal. Which condition is this?

Answer: SAS

Builds on: Classify triangles; angles in a triangle, Translations, reflections and rotations

Leads to: Choose the congruence test (SSS, SAS, ASA, AAS, RHS)

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Find a missing endpoint from a midpoint

CCSS HSG.GPE.B.6England: GCSE Higher Geometry

Example

The midpoint of P(−9, 9) and Q(a, b) is (0, 4). Find b.

(9 + b)/2 = 4 → b = −1

Answer: -1

Builds on: Distance and midpoint between points

Leads to: Find the point that divides a segment in a given ratio

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