Isosceles & right triangles

Japanese school year: Junior high 2

What you learn

Learn the properties of isosceles triangles, such as equal base angles, and the special congruence conditions for right triangles involving the hypotenuse. These are frequently applied in geometric proofs and length calculations. Prior mastery of general triangle congruence conditions is required.

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Key points

This property is used to determine whether a triangle is isosceles. Two sides $AB$ and $AC$ are equal in length if and only if their opposite base angles $\angle B$ and $\angle C$ are equal.

AB = AC \iff \angle B = \angle C

This condition is used to prove that two right triangles are congruent. They are congruent if their hypotenuses ( $AB$ and $DE$ ) and one corresponding acute angle ( $\angle A$ and $\angle D$ ) are equal.

\angle C = \angle F = 90^\circ, \; AB = DE, \; \angle A = \angle D \implies \triangle ABC \equiv \triangle DEF

This condition is used to prove that two right triangles are congruent. They are congruent if their hypotenuses ( $AB$ and $DE$ ) and another pair of corresponding sides ( $AC$ and $DF$ ) are equal.

\angle C = \angle F = 90^\circ, \; AB = DE, \; AC = DF \implies \triangle ABC \equiv \triangle DEF

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Practice 1Coming soon