"Isosceles Triangle" PPT courseware 6

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"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.

Understanding of the definition: A triangle with two equal sides is called an isosceles triangle.

⑴ From "both sides are equal" we get "isosceles triangle".

∵AB=AC,

∴△ABC is an isosceles triangle.

⑵ From "isosceles triangle", we get "both sides are equal".

∵△ABC is an isosceles triangle

∴AB=AC.

Method 1: Draw the center line on the bottom edge

The two base angles of an isosceles triangle are equal.

Known: As shown in the figure, in △ABC, AB=AC.

Prove: ∠B= ∠C.

Prove: Draw the midline AD of the base, then BD=CD

In △BAD and △CAD

AB=AC

BD=CD

AD=AD

∴ △BAD ≌ △CAD (SSS).

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

Method 2: Draw the bisector of the vertex angle

The two base angles of an isosceles triangle are equal.

Known: As shown in the figure, in △ABC, AB=AC.

Prove: ∠B= ∠C.

Proof: Draw the bisector AD of the vertex angle, then ∠1=∠2

In △BAD and △CAD

AB=AC (known)

∠1=∠2 (already made)

AD=AD (common edge)

∴ △BAD ≌ △CAD (SAS).

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

Property Theorem 1

The two base angles of an isosceles triangle are equal.

Abbreviation (equilateral equal angles)

∵AB=AC.

∴∠B=∠C.

Property Theorem 2

The vertex bisectors of an isosceles triangle, the midline on the base, and the height on the base coincide.

(referred to as three lines in one)

Definition: A triangle with three equal sides is called an equilateral triangle.

Relationship: An equilateral triangle is a special isosceles triangle.

Theorem of properties of an equilateral triangle: The angles of an equilateral triangle are all equal, and each angle is equal to 60°.

The two base angles of an isosceles triangle are equal.

A triangle with two equal base angles is an isosceles triangle.

A triangle with two equal angles is an isosceles triangle.

Determination theorem of isosceles triangle:

If a triangle has two equal angles, then the triangle is an isosceles triangle. where the opposite sides of two equal angles are equal.

(referred to as "equal angles and equal sides").

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Update Time: 2024-09-16

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

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