"Congruent Triangles" PPT Courseware 6

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"Congruent Triangles" PPT Courseware 6

think

What are the characteristics of the two figures in each group?

Can overlap, have the same size, and have the same shape

Two figures that can completely overlap are called congruent shapes:

Discuss

(1) Can you still name examples of congruent shapes in life?

(2) If two figures are congruent, must their shapes and sizes be the same?

Characteristics of congruent shapes

Congruent shapes have the same shape and size

in conclusion

We call two figures that can completely overlap as congruent shapes.

Two triangles that completely overlap are called congruent triangles.

When two congruent triangles are overlapped together, the overlapping vertices are called corresponding vertices, the overlapping sides are called corresponding sides, and the overlapping angles are called corresponding angles.

Can you point out the corresponding vertices, corresponding sides, and corresponding angles of the two congruent triangles above?

Representation of congruent triangles

"Congruent" uses the symbol "≌" to indicate that △ABC and △DEF in the figure are congruent.

Written as △ABC≌ △DEF, pronounced as △ABC, all equal to △DEF

When two triangles are congruent, the letters representing the corresponding vertices are usually written in the corresponding positions.

True or False

1) The corresponding sides of congruent triangles are equal and the corresponding angles are equal. ( )

2) Congruent triangles have equal perimeters and equal areas. ( )

3) Triangles with equal areas are congruent triangles. ( )

4) Triangles with equal perimeters are congruent triangles. ( )

Properties of congruent triangles

1. Corresponding sides of congruent triangles are equal

△ABC≌△DEF

AB=DE AC=DF BC=EF

2. Corresponding angles of congruent triangles are equal

△ABC≌△DEF

∠A=∠D ∠B=∠E ∠C=∠F

3. The areas and perimeters of congruent triangles are equal

Please fill in the blank

1. If △AOC≌△BOD, AC=____ ∠A=____

2. If △ABD≌△ACE, BD＝____, ∠BDA＝____

3. If △ABC≌△CDA, AB=____∠BAC=____

In the figure below, △ABO≌△ACO, BO and CO, AB and AC are the corresponding sides.

Express three sets of corresponding sides and three sets of corresponding angles in the form of equations.

In the figure below, △ABO≌△DCO, A and D, B and C are the corresponding vertices. Three sets of corresponding sides and three sets of corresponding angles are expressed in the form of equations.

Compliance feedback:

(1) △ABC≌ △BAD, point A and point B, point C and point D are corresponding points. If AB=6cm, BD=5cm, AD=7cm, then the length of BC is (　)

(A) 7cm (B) 6cm (C) 5cm (D) Unable to determine

(2) In the above question, the corresponding angle of ∠CAB is (　)

(A)∠DAB　 (B) ∠DBA

(C) ∠ DBC (D) ∠ CAD

3. Fill in the form: As shown in the figure, it is known that △ABC≌△ADE,

Think about it: ∠ BAD = ∠ CAE? Why?

Answer: Equal. The reasons are as follows:

∵△ABC≌△ADE (known)

∴∠ BAC= ∠ DAE (corresponding angles of congruent triangles are equal)

∴∠ BAC - ∠ DAC= ∠ DAE - ∠ DAC (equality property)

That is ∠ BAC = ∠ DAE

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Update Time: 2024-09-30

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

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