"Determination of Congruent Triangles" PPT Courseware 2

Description

"Determination of Congruent Triangles" PPT Courseware 2

learning target:

1. Be proficient in using the method of determining congruence of triangles.

2. Master the proof of congruent triangles with special relationships.

Use scissors to cut out two triangles of exactly the same shape and size on the white paper.

Arrange them in terms of translation, rotation, and symmetry to see what special positional relationships the two triangles have.

hint:

1. Parallel line type: Two triangles have one or two sets of corresponding sides that are parallel

2. Intersecting line type: two triangles have a common side or angle.

3. Rotation type: A triangle is formed by rotating another triangle (the center of rotation is the vertex of the triangle)

Time preset and group display:

1. Explore new knowledge independently (5 minutes)

2. Group cooperation to explore example questions (exhibition preparation) (3 minutes)

3. Group presentation: (8 minutes)

4. Summary (2 minutes)

5. Consolidation exercises (8 minutes)

6. Detection (6 minutes)

Explore new knowledge

Proof of congruent triangles with special positional relations

Example 1: Known: As shown in Figure 13-3-12, in △ABC, D is the midpoint of BC,

DE∥AB intersects AC at point E, DF ∥AC intersects AB at point F.

Prove: △BDF≌△DCE.

Example 2: Known: As shown in Figure 13-3-13, in △ABC, D and E are respectively

AB, the midpoint of AC, CF∥AB, intersect the extension line of DE at point F.

Prove: DE=FE

Class summary:

The proof about congruent triangles can be done as follows:

①Observe whether there is a special positional relationship.

②What conclusion can be drawn if it exists?

③Select the triangle judgment method

(Then just prove it according to the standard format!)

Classroom test:

Known: As shown in the figure, take a point E and D on AB and AC each, so that AE=AD, connect BD and CE to intersect at point O, connect AO, ∠1=∠2

Prove: ∠B=∠C

Proof: In △AEO and △ADO

AE=AD(known)

∠1=∠2 (known)

AO=AO (common edge)

∴�AEO≌�ADO(SAS)

∴ ∠AEO=∠ADO EO=DO

∴ ∠BEO=∠CDO

∵ ∠BOE=∠COD (the two vertex angles are equal)

∴ ∠B=∠C

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"Determination of Congruent Triangles" PPT courseware 4:

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Update Time: 2024-07-05

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

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