"Right Triangle" Proof PPT Courseware 2

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"Right Triangle" Proof PPT Courseware 2

Determination of congruence of triangles

Axiom: Two triangles with three corresponding equal sides are congruent (SSS).

Axiom: Two triangles whose sides and angles are equal are congruent (SAS).

Axiom: Two triangles whose angles and included sides are equal are congruent (ASA).

Corollary: Two triangles are congruent (AAS) if the two angles and the opposite side of one of the angles are equal.

Think about it:

Two triangles with equal sides and opposite angles of one of them are congruent?

Two triangles whose sides and opposite angles of one of them are equal are not necessarily congruent.

What if the angle subtended by one of the sides is a right angle?

If the angle subtended by one of the sides is a right angle, then the two triangles are congruent.

Please justify your conclusion.

Decide whether the following propositions are true or false and explain why:

Two acute angles correspond to two congruent right triangles;

The hypotenuse and an acute angle correspond to two congruent right triangles;

Two right triangles with two corresponding equal sides are congruent;

Two right triangles are congruent if one right-angled side and the midline of the other right-angled side are equal.

Determination theorem for congruence of right triangles:

Theorem: Two right triangles are congruent if the hypotenuse and a right side are equal (hypotenuse, right side or HL).

Axiom: Two triangles with three corresponding equal sides are congruent (SSS).

Axiom: Two triangles whose sides and angles are equal are congruent (SAS).

Axiom: Two triangles whose angles and included sides are equal are congruent (ASA).

Corollary: Two triangles are congruent (AAS) if the two angles and the opposite side of one of the angles are equal.

To sum up, the conditions for determining congruence of right triangles can be summarized as:

Two right triangles with equal sides and one acute angle are congruent;

Two right triangles whose sides are equal are congruent;

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Update Time: 2024-11-07

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