4.4

Triangles

Cambridge IGCSE Mathematics (0580)  · Unit 4: Geometry  · 10 flashcards

Triangles is topic 4.4 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Angles in polygons and Parallel lines.  In one line: An equilateral triangle has three sides of equal length. All three interior angles are also equal, each measuring 60 degrees.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 10 flashcards — 7 definitions, 1 key concept and 1 application card — covering the precise wording mark schemes reward.  Use the 7 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

An equilateral triangle and state its key property regarding angles

An equilateral triangle has three sides of equal length. All three interior angles are also equal, each measuring 60 degrees.

Questions this Triangles deck will help you answer

Definition Flip

Define an equilateral triangle and state its key property regarding angles.

Answer Flip

An equilateral triangle has three sides of equal length. All three interior angles are also equal, each measuring 60 degrees.

Definition Flip

What is an isosceles triangle, and what is significant about its base angles?

Answer Flip

An isosceles triangle has two sides of equal length. The angles opposite these equal sides (the base angles) are also equal.

Definition Flip

Describe a scalene triangle and how it differs from equilateral and isosceles triangles.

Answer Flip

A scalene triangle has all three sides of different lengths. Consequently, all three interior angles are also different sizes, unlike equilateral or isosceles triangles.

Key Concept Flip

State the angle sum property for any triangle and illustrate with an example.

Answer Flip

The sum of the interior angles in any triangle is always 180 degrees.

Example: in a triangle with angles 50°, 70°, and 60°, 50 + 70 + 60 = 180.
Definition Flip

Explain the SSS congruence criterion for triangles. Provide an example.

Answer Flip

SSS (Side-Side-Side) states that if all three sides of one triangle are equal in length to the corresponding three sides of another triangle, then the two triangles are congruent. Therefore, they are identical.

Definition Flip

Explain the SAS congruence criterion for triangles, including what 'included angle' means.

Answer Flip

SAS (Side-Angle-Side) states that if two sides and the included angle (the angle between those two sides) of one triangle are equal to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.

Definition Flip

Explain the ASA congruence criterion for triangles, including what 'included side' means.

Answer Flip

ASA (Angle-Side-Angle) states that if two angles and the included side (the side between those two angles) of one triangle are equal to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

Definition Flip

Explain the RHS congruence criterion for right-angled triangles.

Answer Flip

RHS (Right angle-Hypotenuse-Side) states that if the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and corresponding side of another right-angled triangle, then the two triangles are congruent.

Key Concept Flip

Triangle ABC has angles A = 60°, B = 80°. Calculate the measure of angle C.

Answer Flip

Since the angles in a triangle sum to 180°, C = 180° - A - B = 180° - 60° - 80° = 40°. Angle C measures 40 degrees.

Key Concept Flip

Two triangles have sides AB = DE, BC = EF, and CA = FD. Are the triangles congruent? Which congruence criterion applies?

Answer Flip

Yes, the triangles are congruent. The SSS (Side-Side-Side) congruence criterion applies, as all three sides of one triangle are equal in length to the corresponding sides of the other.

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4.3 Parallel lines 4.5 Quadrilaterals

Key Questions: Triangles

Define an equilateral triangle and state its key property regarding angles.

An equilateral triangle has three sides of equal length. All three interior angles are also equal, each measuring 60 degrees.

What is an isosceles triangle, and what is significant about its base angles?

An isosceles triangle has two sides of equal length. The angles opposite these equal sides (the base angles) are also equal.

Describe a scalene triangle and how it differs from equilateral and isosceles triangles.

A scalene triangle has all three sides of different lengths. Consequently, all three interior angles are also different sizes, unlike equilateral or isosceles triangles.

Explain the SSS congruence criterion for triangles. Provide an example.

SSS (Side-Side-Side) states that if all three sides of one triangle are equal in length to the corresponding three sides of another triangle, then the two triangles are congruent. Therefore, they are identical.

Explain the SAS congruence criterion for triangles, including what 'included angle' means.

SAS (Side-Angle-Side) states that if two sides and the included angle (the angle between those two sides) of one triangle are equal to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.

Tips to avoid common mistakes in Triangles

More topics in Unit 4 — Geometry

Triangles sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

triangle equilateral isosceles scalene right-angled angle sum 180 degrees base angles congruent triangles SSS SAS ASA RHS

Key terms covered in this Triangles deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

An equilateral triangle and state its key property regarding angles
Isosceles triangle, and what is significant about its base angles
Describe a scalene triangle and how it differs from equilateral and isosceles triangles
Explain the SSS congruence criterion for triangles. Provide an example
Explain the SAS congruence criterion for triangles, including what 'included angle' means
Explain the ASA congruence criterion for triangles, including what 'included side' means
Explain the RHS congruence criterion for right-angled triangles

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How to study this Triangles deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.