"Isosceles Triangle" PPT courseware

Description

"Isosceles Triangle" PPT courseware

A triangle with two equal sides is called an isosceles triangle

A triangle with three equal sides is called an equilateral triangle

Experimentation and inquiry

(1) Given the base and side of an isosceles triangle, can you use a ruler and compass to make this isosceles triangle ABC?

(2) As shown in Figure 2-38, cut out the isosceles triangle ABC you made. Then fold it in half so that the rays of the two waists AB and AC coincide with each other. Note the intersection point of the fold and the base BC as D. Did you find that the isosceles triangle ABC is an axially symmetrical figure?

(3) In Figure 2-38, according to the basic properties of axial symmetry, what is the relationship between the symmetry axis AD and the base BC? According to the axial symmetry of angles, what is the relationship between ∠BAD and ∠CAD? From this, you find out what is the relationship between the height, midline and bisector of the vertex angle on the base BC of the isosceles triangle ABC?

(4) Using the axial symmetry of the isosceles triangle, did you find that ∠B and ∠C are equal?

What properties can you derive from this about the base angles of an isosceles triangle?

(5) Can you summarize the properties of an isosceles triangle?

Conjecture and Argument

The two base angles of an isosceles triangle are equal.

Referred to as "equilateral equal angles"

Known: In △ABC, AB=AC

Prove: ∠B=C

Proof: Draw the bisector AD of the vertex angle,

Then there is ∠1=∠2

In △ABD and △ACD

AB=AC

∠1＝∠2

AD=AD (common edge)

∴ △ABD≌ △ACD (SAS)

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

Inductive conclusion

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

(abbreviation: equilateral equal angles)

Expressed in symbolic language as:

In △ABC,

∵ AC=AB (known)

∴ ∠B=∠C (equilateral opposite angles)

Property 2

The bisector of the vertex of an isosceles triangle, the midline of the base, and the height of the base coincide with each other.

Also known as "three lines in one".

Expressed in symbolic language as:

In △ABC, AB =AC, point D is on BC

1. ∵AD ⊥BC

∴∠ 1=∠2, BD=DC.

2. ∵AD is the angle bisector,

∴AD⊥BC, BD=DC.

3. ∵AD is the center line,

∴ AD⊥BC, ∠1=∠2.

Properties of isosceles triangle

An isosceles triangle is an axially symmetrical figure. The axis of symmetry of an isosceles triangle is the perpendicular bisector of the base.

The vertex bisector of an isosceles triangle, the height on the base, and the midline on the base coincide (also called three lines in one).

The two base angles of an isosceles triangle are equal. (referred to as "equilateral angles")

Challenge yourself

As shown in Figure 2-42, in Rt△ABC, ∠C=90º, fold the right-angled side BC along a straight line passing through point B, so that point C falls at point D on the hypotenuse AB, what is ∠A? When degrees, point D is exactly the midpoint of AB? Explain your conclusion.

Class summary

1. An isosceles triangle is an axially symmetrical figure. The axis of symmetry of an isosceles triangle is the vertical bisector of the base.

2. The vertex bisector of an isosceles triangle, the height on the base and the midline on the base coincide (three lines combined into one)

3. The two base angles of an isosceles triangle are equal.

Class exercises

Exercise 1

1. Among the following figures, which one is not an axially symmetric figure ( )

A. Isosceles triangle B. Line segment

C. Obtuse angle D. Right triangle

2. The base angle of an isosceles triangle is twice the vertex angle, then the number of base angles is ( )

A. 36° B. 32° C. 64° D. 72°

3. The axis of symmetry of an isosceles triangle is the vertical bisector of the base.

Exercise 2.

1. The angle formed by the height of the base of an isosceles triangle and one waist is equal to ( )

A. vertex angle B. half of vertex angle

C. Twice the top angle D. Half the bottom angle

2. The lengths of both sides of an isosceles triangle are 2cm and 5cm respectively. Then the perimeter of this triangle is ( )

A. 9cm B. 12cm

C. 9cm or 12cm D. Between 9cm and 12cm

3. As shown in the figure, in isosceles △ABC, AD⊥BC is at D. It is known that DC=2cm and AB=3cm, then the circumference of △ABC is 10cm.

4. Known: One angle of an isosceles triangle is 80°, then its other two angles are 50°, 50° or 80°, 20°.

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"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: 2024-06-20

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

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