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

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

Knowledge review: Determining conditions for congruence of triangles

Two triangles with three corresponding equal sides are congruent (can be abbreviated as "side-side-side" or "SSS")

Expressed in mathematical language:

In △ABC and △DEF

AB=DE (known)

BC=EF (known)

CA=FD (known)

∴ △ABC ≌△ DEF (SSS)

Both sides and their angle

Make a triangle with two sides of 15cm and 10cm and an included angle of 450. Cut it out and compare it at the same table.

Drawing method: 1. Draw ∠MAN=45°;

2. Intercept AC=15cm on the ray AM;

3. Intercept AB=10cm on ray AN;

4. Connect BC. △ABC is the triangle created.

Discover:

If two triangles have ____ and their ____ correspondences are equal, then the two triangles are congruent.

Can it only be the two sides and the angle between them?

Is it okay to have two sides and one side diagonally?

Two sides and the opposite angle of one side

Make a triangle with two sides of 15cm and 12cm, and the diagonal angle of the 12cm side is 450

1. Draw ∠MAN=45°;

2. Intercept AC=15cm on the ray AM;

3. With point C as the center and a length of 12cm as the radius, draw a circle and intersect AN at point B.

4. △ABC is the triangle made

1. Known: As shown in the figure, AD∥BC, AD=CB, verify: DC=BA.

【Proof】∵ AD∥BC,

∴ ∠1=∠2 (the two straight lines are parallel and the internal offset angles are equal).

In △DAC and △BCA,

AD=CB (known)

∠1=∠2 (known)

AC=CA (common edge)

∴ △ADC≌△CBA(SAS).

∴DC=BA

Class summary:

What did you learn in this class?

1. "Single Corner (SAS)"

2. The problem of equal angles or equal line segments can generally be solved by congruence.

Additional exercises:

In △ABC, AB=AC,

AD is the angle bisector of ∠BAC.

So are BD and CD equal? Why?

Solution: equal

Reason: ∵AD is the angle bisector of ∠BAC

∴∠BAD=∠CAD

∵AB＝AC

∠BAD=∠CAD

AD＝AD

∴△ABD≌△ACD (SAS)

∴BD＝CD

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Update Time: 2024-07-01

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