"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 6

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"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 6

Review the past and learn the new

1. What are similar triangles?

Two triangles whose angles are equal and whose sides are proportional are called similar triangles

2. What are congruent triangles?

Triangles correspond to equality, and two triangles whose sides correspond to equality are congruent.

3. What methods do we commonly use to determine whether two triangles are congruent?

SSS, SAS, ASA (AAS), HL (Rt△)

Two triangles are similar if two angles of one triangle are equal to two angles of another triangle.

(Two triangles with equal angles are similar)

Geometric language: In △ABC and △A″B″C″,

∵∠A＝∠A″, ∠B＝∠B″,

∴△ABC∽△A″B″C″

Which of the following statements about triangle similarity is incorrect ( )

A. Two isosceles triangles with one corresponding base angle are similar;

B. Two isosceles triangles with one corresponding equal angle are similar;

C. All equilateral triangles are similar;

D. Two isosceles triangles with equal vertex angles are similar.

1. As shown in the figure, in ΔABC and ΔDEF, ∠A=40o, ∠B=80o, ∠E=80o, ∠F=60o. Are ΔABC and ΔDEF similar? Why?

Solution: ΔABC∽ΔDEF

in ΔABC

Because ∠A=40o, ∠B=80o,

So ∠C=180o-(40o+80o)=60o

In ΔABC and ΔDEF

Because ∠B=∠E, ∠C=∠F

So ΔABC∽ΔDEF

2. As shown in the figure, DE∥BC intersects AB and AC at points D and E respectively. Are △ADE and △ABC similar? Why?

Solution: △ADE∽△ABC.

In △ADE and △ABC,

Because DE∥BC,

So ∠ADE=∠B, ∠AED=∠C

So △ADE∽△ABC

summary

1. Ask students to talk about their gains and experiences from this class.

2. In this lesson, we explored the conditions for judging the similarity of two triangles:

Two triangles with equal angles are similar.

When a straight line parallel to one side of a triangle intersects the other two sides (or extensions of both sides), the triangle formed is similar to the original triangle.

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Update Time: 2024-10-19

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