"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware

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"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware

review

What two triangles are called congruent triangles? What does it mean?

Answer: Two triangles that can completely overlap are called congruent triangles.

Triangle congruence determination theorem (1)

Two triangles are congruent if two sides of one triangle and their angle are correspondingly equal to two sides and their angle of another triangle.

Example 1: As shown in the figure: AB=DC, ∠ABC= ∠DCB,

Prove: �ABC≌ �DCB

Analysis: Question review: AB=DC, ∠ABC= ∠DCB.

Map review: BC is the common edge of �ABC and �DCB.

Review conclusion: �ABC≌ �DCB ---- SAS

Proof: In �ABC and �DCB Note:

AB=DC (known) 1. In which two triangles?

∠ABC= ∠DCB (known) 2. The conditions are given in terms of sides, angles and sides.

BC=CB (common side) 3. Correspondence.

∴ �ABC≌ �DCB (SAS)

Example 2: Known: AB=AC, E and F are on AB and AC respectively and AE=AF

Prove: �ABF≌�ACE

Review question: AB=AC, AE=AC.

Drawing review: ∠A is the common angle between �ABF and �ACE.

Review conclusion: �ABF≌�ACE---- SAS

Proof: In �ABF and �ACE

AB=AC (known)

∠A= ∠A (common angle)

AE=AC (known)

∴ �ABF≌�ACE (SAS)

summary

What did the students gain from today’s study?

1. Clamp one corner from both sides.

2. When looking for corresponding parts, you must follow SAS standards.

3. Correspondence: Two congruent triangles, the letters must correspond one to one.

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Update Time: 2024-10-08

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