"Isosceles Triangle" Axis Symmetry PPT Courseware

Description

"Isosceles Triangle" Axis Symmetry PPT Courseware

A triangle with two equal sides is called an isosceles triangle.

In an isosceles triangle, the two equal sides are called the waist, the other side is called the base, the angle between the two waists is called the vertex angle, and the angle between the waist and the base is called the base angle.

Exploration and verification:

Property 1. The two base angles of an isosceles triangle are equal. (equilateral angles)

Known: In △ABC, AB=AC

Proof: Draw the midline AD on the side of base BC.

In △ABD and △ACD:

AB=AC (known)

BD=DC (drawing)

AD=AD (common edge)

∴△ABD≌△ACD (SSS)

∴∠B=∠C (corresponding angles of congruent triangles are equal)

Property 2: The vertex bisector of an isosceles triangle, the midline on the base, and the base on the base are usually said to be the "three lines in one" of the isosceles triangle)

1. The bisector of the vertex angle of an isosceles triangle is both the midline of the base and the height of the base.

Application format: ∵AB＝AC ∠1＝∠2 (known)

∴BD＝DC AD⊥BC (the three lines of the isosceles triangle merge into one)

2. The midline of the base of an isosceles triangle is both the height of the base and the bisector of the vertex angle.

Application format: ∵AB＝AC BD＝DC (known)

∴AD⊥BC ∠1＝∠2 (the three lines of the isosceles triangle merge into one)

3. The height of the base of an isosceles triangle is both the midline of the base and the bisector of the vertex angle.

Application format: ∵AB＝AC AD⊥BC (known)

∴BD＝DC ∠1＝∠2 (the three lines of the isosceles triangle merge into one)

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For more information about the "Axisymmetric Isosceles Triangle" PPT courseware, please click the Axisymmetric ppt Isosceles Triangle ppt tag.

"Isosceles Triangle" PPT Courseware 6:

"Isosceles Triangle" PPT Courseware 6

The concept of isosceles triangle

A triangle with two equal sides is called an isosceles triangle.

Two equal sides are called waist

The other side is called the bottom side

The angle between the two waists is called the vertex angle

The angle between the waist and the bottom is called the bottom angle...

"Isosceles Triangle" PPT courseware 5:

"Isosceles Triangle" PPT courseware 5 Experimental exploration Draw an isosceles triangle ABC on the paper, fold the paper in half so that its two waists AB and AC coincide, mark the intersection of the fold and the base as D, and then unfold the paper To lay the ground, think about the following questions: Question (1) Isosceles III..

"Isosceles Triangle" PPT courseware 4:

"Isosceles Triangle" PPT Courseware 4 Course Standard Requirements Explore and prove the property theorem of an isosceles triangle: The two base angles of an isosceles triangle are equal; the altitude line, midline and vertex angle bisector on the base coincide (three lines merge into one). Explore and master the determination theorem of isosceles triangles..

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Update Time: 2024-11-26

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 1 industry PPT template

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