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.
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
- › State the angle sum property for any triangle and illustrate with an example.
- › Two triangles have sides AB = DE, BC = EF, and CA = FD. Are the triangles congruent? Which congruence criterion applies?
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.
State the angle sum property for any triangle and illustrate with an example.
The sum of the interior angles in any triangle is always 180 degrees.
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.
Explain the ASA congruence criterion for triangles, including what 'included side' means.
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.
Explain the RHS congruence criterion for right-angled triangles.
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.
Triangle ABC has angles A = 60°, B = 80°. Calculate the measure of angle C.
Since the angles in a triangle sum to 180°, C = 180° - A - B = 180° - 60° - 80° = 40°. Angle C measures 40 degrees.
Two triangles have sides AB = DE, BC = EF, and CA = FD. Are the triangles congruent? Which congruence criterion applies?
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.
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
- ● Remember: to go from length ratio to volume ratio, you need to CUBE the length scale factor (LSF³).
- ● Review triangle congruence rules: RHS stands for Right angle, Hypotenuse, and Side — make sure you can apply each rule correctly.
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.
10 flashcards
9 flashcards
10 flashcards
9 flashcards
9 flashcards
9 flashcards
9 flashcards
9 flashcards
9 flashcards
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.
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.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Triangles deck
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