"Properties of Isosceles Triangles" Axisymmetric PPT Courseware

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"Properties of Isosceles Triangles" Axisymmetric 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.

Small scale chopper

1. If the waist of an isosceles triangle is 3cm and the base is 4cm, then its perimeter is __________;

2. One side of an isosceles triangle is 3cm long and the other side is 4cm long. Then its perimeter is __________;

3. One side of an isosceles triangle is 3cm long and the other side is 8cm long. Then its perimeter is __________.

Is an isosceles triangle an axially symmetrical figure?

An isosceles triangle is an axially symmetrical figure, and the axis of symmetry is the straight line where the bisector of the vertex angle lies.

Distinguish between right and wrong

1. The vertex angles of an isosceles triangle must be acute angles. (X)

2. The base angle of an isosceles triangle may be acute, right or obtuse. (X)

3. The bisector of the vertex angle of an isosceles triangle must be perpendicular to the base. (√)

4. The angle bisectors, midlines and heights of an isosceles triangle coincide with each other. (X)

5. The midline on the base of an isosceles triangle must bisect the vertex angle (√)

As shown in the figure, in △ABC, AB=AC, point D is on AC, and BD=BC=AD. Find the degrees of each angle of △ABC.

Solution: ∵AB=AC, BD=BC=AD,

∴∠ABC=∠C=∠BDC, ∠A=∠ABD (equilateral angles)

Assume ∠A=x, then ∠BDC= ∠A+ ∠ABD=2x,

Thus ∠ABC= ∠C= ∠BDC=2x,

So in △ABC,

There is ∠A+∠ABC+∠C=x+2x+2x=180°,

The solution is x=36°,

In △ABC, ∠A=36°, ABC=∠C=72°

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Update Time: 2024-09-23

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

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