"How to Determine Congruence of Triangles" PPT Courseware 3

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"How to Determine Congruence of Triangles" PPT Courseware 3

review

1.What are congruent triangles?

2. What methods have we learned to determine whether triangles are congruent?

①Definition

②Surface (SAS):

Two triangles are congruent if their sides and their included angles are equal.

Create scenarios and introduce examples

A piece of triangular cardboard used for teaching was accidentally torn, as shown in the picture. Can you make a new teaching aid of the same size as the original? Can the original shape of the triangle be restored?

If two triangles have equal angles and one side, how many possible situations are there?

1. The included sides of the two angles are equal.

2. There are two angles that are equal to the opposite side of one of the angles.

3. Two angles are correspondingly equal, and the included side of one triangle is equal to the opposite side of a corresponding angle in another triangle.

Three situations in total

Exploration 1: Let’s first explore whether the two triangles are congruent when the included sides of the two angles are equal.

1. As shown in the figure: in △ABC and △A´B´C´, BC=B´C´, ∠B=∠B´, add the condition ∠C＝∠C´

Are △ABC and △A´B´C´ congruent?

2. Observe carefully: Place △ABC on △A´B´C´ so that points B and B coincide, side BC falls on BC, and point A and point A are on the same side of BC.

3. What conclusion can you draw? Give reasons.

Judgment method 2

Two triangles whose angles and included sides are congruent

(Abbreviated as "Angle Corner" or "ASA").

Expressed in symbolic language as:

In △ABC and △DEF

∠A=∠D

AB=DE

∠B=∠E

∴ △ABC≌△DEF (ASA)

Exploration 2

Are two triangles congruent with two angles and equal sides to one of the angles?

As shown in the picture: In △ABC and △DEF, ∠A=∠D, ∠B=∠E, BC=EF, are △ABC and △DEF congruent?

Can you use corner conditions to illustrate your conclusion?

Reason: Because ∠A＋∠B＋∠C=180°

∠D＋∠E＋∠F=180°

And because ∠A=∠D, ∠B=∠E

So ∠C=∠F

In △ABC and △DEF

According to the ASA,

So △ABC≌△DEF(ASA)

summary

1. Can you summarize the methods we have learned to determine whether triangles are congruent?

2. Choose the appropriate method according to the meaning of the question.

3. To make line segments or angles equal, it is necessary to determine that the two triangles in which they are located are congruent.

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For more information about the PPT courseware "How to Determine the Congruence of Triangles", please click the "How to Determine the Congruence of Triangles" ppt tag.

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"How to Determine Congruence of Triangles" PPT Courseware 2:

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Update Time: 2024-09-06

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 1 industry PPT template

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