"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware 4

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"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware 4

review

What two triangles are called congruent triangles?

How to represent congruent triangles? What should I pay attention to?

What are the properties of congruent triangles?

We know that if two triangles are congruent, then their corresponding sides are equal and their corresponding angles are equal.

Conversely, what conditions are met when two triangles are congruent, that is, how many sets of sides or angles they have are equal?

Discuss

1. When two triangles have only one set of equal sides or angles, are they congruent?

Conclusion: Two triangles with only one corresponding side or angle are not necessarily congruent.

2. When two triangles have only 2 sets of equal sides or angles, are they congruent?

3. When two triangles have three sets of equal sides or angles, are they congruent?

Activity 1

As shown in the picture, use a rectangular piece of paper to subtract a right triangle. How can you make the right triangles cut out by the class all congruent?

(1) What is your best way to make all the cuts of the class equal? Tell me about your method.

(2) Cut out the right triangle and verify it among the students in the group

Example 1 As shown in the figure, AB=AD, ∠BAC= ∠DAC, are △ABC and △ADC congruent? Why?

Reflection on problem solving:

1. Write which two triangles it is in;

2. The conditions are given in terms of sides, angles, and sides, and written accordingly.

3. Determining whether two line segments are equal or two angles are equal can be obtained from the congruence of the two triangles in which they are located.

Exercise 1. It is known that: AB=AC, E and F are on AB and AC respectively and AE=AF. So is △ABF≌△ACE? Why?

Review question: AB=AC, AE=AC

Drawing review: ∠A is the common corner of △ABF and △ACE

Review conclusion: △ABF≌△ACE(SAS)

2. As shown in the figure, AC and BD intersect at point O. It is known that OA=OC and OB=OD. Explain the reason why △AOB≌△COD

Note: Make full use of conditions such as "common sides", "common angles", and "equal opposite vertex angles" in graphics.

3. As shown in the figure: AB=DC is known. To determine △ABC≌ △DCB, one more condition needs to be added: ∠ABC= ∠DCB

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"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware 3:

"Exploring the Conditions for Triangle Congruence" Triangle PPT Courseware 3 Knowledge Review: Determination Conditions for Triangle Congruence Three sides corresponding to two equal triangles are congruent (can be abbreviated as side-side-side or SSS) Expressed in mathematical language: In △ABC and △ AB=DE in DEF (known..

"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware 2:

"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware 2 Review: 1. What is a triangle? A figure formed by connecting three line segments end to end; 2. What is a congruent triangle? What are the properties of congruent triangles? Triangles that can completely overlap. Congruent triangles..

"Exploring the conditions for congruence of triangles" Triangle PPT courseware:

"Exploring the Conditions for Congruence of Triangles" Triangle PPT Courseware Review What kind of 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) If a three...

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Update Time: 2024-11-23

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