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"Isosceles Triangle" PPT Courseware 2
Review review:
What are the properties of an isosceles triangle?
An isosceles triangle is an axially symmetrical figure, and the straight line where the bisector of the vertex angle is located is its axis of symmetry.
1. The two base angles of an isosceles triangle are equal
(referred to as "equilateral equal angles")
2. The vertex bisector of an isosceles triangle, the midline on the base, and the height on the base coincide with each other. (referred to as "three lines in one")
Question: In a triangle, if two angles are equal, do the sides opposite the two angles also have to be equal?
1. As shown in the figure, if you draw a cross-section AB arbitrarily on a rectangular piece of paper, are the obtained ∠1 and ∠2 equal? Why?
2. As shown in the figure, fold the paper strip along the section line AB. In the obtained △ABC, there is still ∠1 = ∠2. Measure the lengths of sides AC and BC. What do you find?
Draw line segment AB on a piece of tissue paper, and use a protractor to draw two equal acute angles ∠BAM and ∠ABN on the same side of AB. Assume AM and BN intersect at point C, measure the lengths of AC and BC, or fold paper using ∠BAM coincides with ∠ABN. Do you and your classmates come to the same conclusion?
A triangle with two equal angles is an isosceles triangle. (referred to as "equal angles and equal sides").
practise
1. In △ABC, ∠A=80°, ∠B=50°, then what triangle is △ABC? Why?
2. In △ABC, ∠A=42°, when ∠C= ______, △ABC is an isosceles triangle.
3. As shown in the figure, AB=AD, ∠ABC=∠ADC. Are BC and DC necessarily equal? Why?
Known: As shown in the figure, in △ABC, AB=AC, point D is on AC, and BD=BC=AD. Please indicate how many isosceles triangles there are in the figure?
Variation 1: Point out the equal angles in the figure.
Variation 2: Find the angles of ABC.
Challenge yourself
(1) In Example 4, if the parallel lines ED passing through point O as base BC intersect AB AC at point ED respectively.
In addition to △ABC and △OBC, which triangles are isosceles?
(2) In (1), if AB≠AC and other conditions remain unchanged, is there an isosceles triangle in the picture? Give reasons.
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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..