"Determination of Congruence of Right Triangles" PPT Courseware

Description

"Determination of Congruence of Right Triangles" PPT Courseware

learning target

1. Can use "HL" to determine whether two right triangles are congruent.

2. Knowing the hypotenuse and right angle, use a ruler to draw a right triangle.

Learning points:

A special way to understand congruent right triangles "HL". and will be applied.

Learning difficulties:

Given the lengths of the hypotenuse and the right angle, draw a right triangle.

Quick answer

1. Corresponding sides of congruent triangles -------,, corresponding angles -------

2. The methods for determining the congruence of triangles include: SAS, ASA, AAS, SSS

Observe and think

As shown in the figure, in Δ ABC and Δ A'B'C', ∠ C= ∠ C'=RT ∠ AB=A'B', AC=A'C', indicating that Δ ABC and Δ A'B'C' are congruent reasons.

Analysis: AC=A’C’, regardless of the positions of RT Δ ABC and RT Δ A’B’C’. We can always obtain a figure by performing rotation, translation, and axial symmetry transformation, as shown in the figure, that is, A'C' and AC coincide with each other, and point B' and point B are on both sides of AC respectively. Can you prove it?

Solution ∵ ∠ 1= ∠ 2=90 °

∴ BCB’ is on the same straight line, AC ┴ BB’∵ AB=A’B’

∴ BC=B’C’ (the three lines of an isosceles triangle merge into one)

∵ AC=A’C’ (common side)

∴ RTΔABC ≌ RTΔA’B’C’ (SSS)

example

Given the right side and the hypotenuse, use a ruler and compass to construct a right triangle

Known: line segments a, c(a�c)

Find: △ABC, make ∠C=90°,

Right angle side CB=a, hypotenuse AB=c.

Analysis: First draw the side BC. Since ∠C is a right angle, you can draw the ray where the other right angle side is located. From AB=c, you can determine the point A.

draw a picture

Are you smart enough to draw it?

Drawing method: 1. Draw ∠MCN=90 °.

2. Take CB=a on ray CM.

3. Draw an arc with B as the center and c as the radius. The intersection line CN is at point A.

4 Link AB.

△ABC is the right triangle to be drawn.

Class summary:

1. Determination of right-angled triangles: Two right-angled triangles are congruent if the hypotenuse and a right-angled side are equal.

2. Properties of the bisector of an angle: The interior of an angle, the point equidistant from both sides of the angle, is on the bisector of the angle.

Keywords: teaching courseware for determining the congruence of right-angled triangles, download the eighth-grade mathematics PPT courseware from Hebei Education Edition, download the eighth-grade mathematics slide courseware, download PPT courseware for determining the congruence of right-angled triangles, .PPT format;

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File Info

Update Time: 2024-10-02

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

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