"Properties of Angle Bisectors" Congruent Triangles PPT Courseware 2

Description

"Properties of Angle Bisectors" Congruent Triangles PPT Courseware 2

Observe and understand practices, explore and think about proof methods:

Method: 1. With ____ as the center and the length of ______ as the radius, draw an arc that intersects both sides of the angle at points C and D respectively;

2. Draw an arc with _____ as the center of the circle and the length of __________ as the radius. The two arcs intersect at a point ____ within ∠AOB;

3. Construct ray _____; _____ is the ray you want to construct.

Explore the properties of angle bisectors

(1) Experiment: Draw an ∠AOB, use a ruler and compass to draw the bisector OP of ∠AOB, and draw PD through P ⊥ OA, PE ⊥ OB

Question: ① Compare the size relationship between PD and PE (measure one by one). PD=PE

②Change to a new position and see what happens?

(2) Conjecture: The distance from the point on the bisector of the angle to both sides of the angle is equal.

(3) Verify the conjecture that the distance from the point on the bisector of the angle to both sides of the angle is equal.

Use conclusions to solve problems

practice

1. As shown in the picture, in order to promote the development of local tourism, a resort is to be built on a flat land surrounded by three highways. To make the distance between the resort and the three highways equal, where should it be built?

think about it

When determining the location of a resort, is it necessary to draw the bisectors of the three angles? How did you think about it? How did you prove it?

2. The straight lines represent three intersecting highways. Now we want to build a cargo transfer station, which is required to be equidistant from the three highways. The available addresses are: ( )

A. One place B. Two places

C. Three places D. Four places

Analysis: Since there is no restriction on where to choose the location, there are four required addresses.

Class summary

A point equidistant from both sides of an angle is on the bisector of the angle.

Expressed in mathematical language as:

∵ QD⊥OA, QE⊥OB, QD=QE.

∴Point Q is on the bisector of ∠AOB.

Points on the bisector of an angle are equidistant from both sides of the angle.

Expressed in mathematical language as:

∵ QD⊥OA, QE⊥OB, point Q is on the bisector of ∠AOB

∴ QD＝QE

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Update Time: 2024-09-16

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

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