"Using Triangle Congruence to Measure Distance" Triangle PPT Courseware 3

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"Using Triangle Congruence to Measure Distance" Triangle PPT Courseware 3

1. Review old knowledge

1. What are the necessary conditions to prove that two triangles are congruent?

(1) "SSS": Two triangles with three equal sides are congruent.

(2) "ASA": Two triangles whose two angles and their included sides are equal are congruent.

(3) "AAS": Two triangles whose two angles and the opposite side of one of the angles are equal are congruent.

(4) "SAS": Two triangles whose two sides and their included angles are equal are congruent.

1. Use congruence to make angle bisectors.

As shown in the figure, take OM=ON on sides OA and OB respectively, and move the square ruler so that the same scales on both sides of the square ruler coincide with M and N respectively. The ray OC passing through the vertex C of the square ruler is the bisector of ∠AOB. Why?

2. Use congruence to measure distance.

For practical problems, some line segments or angles are difficult to measure, but using the equal sides of congruent triangles can solve the problem by converting the unmeasurable sides into measurable sides.

Steps to design a measurement plan:

1. Draw the measurement pattern

2. Write down the steps of measurement (expressed in letters)

3. Calculate distance (using the process of reasoning)

summary

In this lesson we learned to use the properties of congruent triangles to measure distances

1. First clarify the actual problem and apply the geometric knowledge.

2. Convert practical problems into geometric problems.

3. Analyze the known conditions based on the graphics and the meaning of the question.

4. Use the knowledge of congruent triangles to explain.

Note: During the measurement process, attention should be paid to utilizing existing conditions and selecting appropriate methods. The more convenient and accurate the measurement method, the better.

Do it and see who is faster!

1. As shown in the figure, to measure the distance between two opposite points A and B on both sides of the river, first take two points C and D on the vertical line BF of AB, so that CD = BC, and then determine the vertical line DE of BF. It can be proved that △ EDC≌△ABC, we get ED=AB. Therefore, the measured length of ED is the length of AB. The reason for determining △EDC≌△ABC is ( )

A.SSS B.ASA C.AAS D.SAS

Class summary

1. Knowledge:

The purpose of using congruent triangles to measure distances is to change unmeasurable distances into measurable distances.

Basis: properties of congruent triangles.

Key: Construct congruent triangles.

2. Methods: (1) Construct congruent triangles using the extension method; (2) Construct congruent triangles using the perpendicular method.

3. Mathematical thinking:

Establish the idea of ​​using congruent triangles to construct mathematical models to solve practical problems.

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For more information about the PPT courseware "Measuring the Distance of Triangles Using Triangle Congruences", please click the "Measuring Distances of Triangles Using Triangles Congruent PPT" ppt tag.

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"Measuring Distance Using Triangle Congruence" Triangle PPT Courseware 2:

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Update Time: 2024-11-20

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

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