"Angle Bisector" PPT Courseware 4

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"Angle Bisector" PPT Courseware 4

ruler and compass as bisector of angle

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

Art style:

1. Take O as the center of the circle, draw an arc with an appropriate length as the radius, intersect OA at M, and intersect OBN at.

2. Take M and N as the center of the circle respectively. If the length greater than 1/2 MN is the radius, draw an arc. The two arcs intersect at C inside ∠AOB.

3. For ray OC.

Ray OC is what is required.

discount

Fold the AOB in half, then fold it into a right triangle (making the first crease the hypotenuse), then unfold it and observe the three creases formed by the two folds. What conclusion can you draw?

You can see that the first crease is the bisector OC of AOB, the two creases PD formed by the second fold, and PE are the distances from a point on the bisector of the angle to both sides of AOB. These two distances are equal.

Properties of angle bisectors:

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

in conclusion:

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

Example: Known: As shown in the figure, the angle bisectors BM and CN of △ABC intersect at point P.

Prove: The distances from point P to three sides AB, BC, and CA are equal.

Prove: Through the point P, draw PD, PE, and PF perpendicular to AB, BC, and CA respectively, and the perpendicular feet are D, E, and F.

∵BM is the angle bisector of △ABC, and point P is on BM

∴PD=PE

(A point on the angle bisector is equidistant from both sides of the angle)

In the same way PE=PF.

∴ PD=PE=PF.

That is, from point P to edges AB, BC,

CA distance is equal

1: Draw the angle bisector of a known angle;

and draw a perpendicular to a known straight line;

2: Properties of angle bisectors:

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

3: Judgment conclusion of angle bisector:

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

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For more information about the PPT courseware "Angle Bisectors", please click the "Angle Bisectors" ppt tab.

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Update Time: 2024-07-03

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

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