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

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

Part One: Learning Objectives

1. Be able to use the congruence of triangles to solve practical problems and understand the connection between mathematics and real life.

2. Able to think and express in an organized manner in the process of solving problems.

Using triangle congruence to measure distance PPT, part 2: activity exploration

Exploration: Use triangle congruence to measure distances

This smart Eighth Route Army soldier’s method is as follows:

He stood facing the direction of the bunker, then adjusted his hat so that his line of sight through the brim of the hat fell right on the bottom of the bunker; then, he turned an angle and maintained the same posture, and now his line of sight fell on a certain point on the shore where he was; Then, he used a walking test to measure the distance between himself and that point. This distance was the distance between him and the bunker.

(1) What are the known conditions in the method described by the soldier?

It can be seen from the method described by the soldier: the height of the soldier AH remains unchanged, the soldier is perpendicular to the ground (AH⊥BC); the perspective ∠HAC=∠HAB, what the soldier wants to measure is the enemy bunker (B) and our army's position (H ), the soldier concluded that as long as the length of HC is measured as required (as shown in the picture) (i.e. BH=HC)

(2) Please use the mathematical knowledge you have learned to explain the reason why BH=CH.

Think about it:

As shown in the picture, two points A and B are located at two ends of a pond. Xiao Ming wanted to use a rope to measure the distance between A and B, but the rope was not long enough. An uncle helped him come up with this idea:

First, pick a point C on the ground that can directly reach points A and B. Connect AC and extend it to D so that CD=CA; connect BC and extend it to E so that CE=CB. Connect DE and measure its length. The length of DE is the distance between A and B.

Using triangle congruence to measure distance PPT, the third part: draw inferences from one example

1. Extend the congruent method measuring distance.

As shown in the figure, take a point C on one side of the pond, connect AC and BC, and extend AC to point D, extend BC to point E, so that CD=AC, CE=BC, connect ED, then the length of ED is the two ends of the pond. The distance between A and B.

(2) Parallel congruence method.

As shown in the figure, take a point D on one side of the pond and connect it to AD. Draw BC∥AD through point B, and make BC=AD and connect DC. Then the length of DC is the distance between A and B at the two ends of the pond.

(3) Vertical congruence method.

As shown in the figure, take a point D on one side of the pond and connect AD and BD. AD⊥BD must be satisfied here. Extend AD to point C so that CD=DA and connect CB. Then the length of CB is A and B at both ends of the pond. distance between.

Using triangle congruence to measure distance PPT, part 4: analysis of examples

For example: As shown in the picture, Xiao Ming has a glass container in his home. He wants to measure its inner diameter? But he couldn't put the scale in to measure directly, so he connected the midpoints of two small wooden bars AB and CD of equal length. The wooden bars could rotate freely around the midpoint O, so as long as the distance between A and C was measured, You can know the inner diameter of the glass container. Do you know the reason? Please explain the reason.

Solution: As shown in the figure: connect AC, BD,

In △ODB and △OCA,

AO=BO, ∠AOC=∠BOD, CO=DO

∴△ODB≌△OCA (SAS),

∴BD=AC．

Therefore, as long as the distance between A and C is measured, the inner diameter of the glass container can be known.

Using triangle congruence to measure distance PPT, Part 5: In-class detection

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

2. As shown in the figure, Xiao Ming designed a caliper to measure the inner diameter AB of the workpiece. Question: In the design of the caliper, which of the following conditions should be met by AO, BO, CO, and DO? ( )

A. AO=CO B. BO=DO

C. AC=BD D. AO=CO and BO=DO

3. To build a bridge at points A and B on both sides of the pond, if you want to measure the distance between points A and B, as shown in the figure, find a point P where A and B are visible, connect AP and extend to D, make PA=PD, connect BP and extend to C, make BP=PC. If CD=35m is measured, it is determined that AB is also 35m. Explain the reason;

Using triangle congruence to measure distance PPT, Part 6 content: Class summary

What did you learn in this lesson?

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.Method

(1) Use the extension method to construct congruent triangles;

(2) Construct congruent triangles using the vertical method.

(3) Parallel method to construct congruent triangles

Using triangle congruence to measure distance PPT, Part 7: Personalized homework

1. During class, Xiao Ming was playing with the teacher’s isosceles triangle and accidentally fell between two walls, as shown in the picture.

Verify: △ADC≌△CEB．

2. As shown in the figure, there is a piece of right-angled triangle paper with two right-angled sides AC=5cm and BC=10cm. Fold △ABC so that point B coincides with point A. The fold is DE, then the perimeter of △ACD is ( )

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For more information about the PPT courseware "Triangles Using Triangle Congruence to Measure Distance", please click on the Triangle PPT Using Triangle Congruence to Measure Distance PPT tag.

"Using Triangle Congruence to Measure Distance" Triangle PPT Teaching Courseware:

"Using Triangle Congruence to Measure Distances" Triangle PPT Teaching Courseware Part One Content: Learning Objectives 1. Review and summarize the judgment and properties of triangle congruence; 2. Be able to measure the distance between two points based on triangle congruence and solve practical problems in learning Key points and difficulties...

"Using Triangle Congruence to Measure Distance" Triangle PPT Download:

"Using Triangle Congruence to Measure Distances" Triangle PPT Download Part One Content: Learning Objectives 1. Be able to use the congruence of triangles to solve practical problems and understand the connection between mathematics and real life. 2. Be able to think in an organized manner in the process of solving problems and express...

"Using Triangle Congruence to Measure Distance" Triangle PPT:

"Using Congruent Triangles to Measure Distances" Triangle PPT Part 1 Content: Think About It 1. What are congruent triangles? Two triangles that can completely overlap are called congruent triangles. 2. What methods have we learned to determine whether two triangles are congruent? side..

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Update Time: 2024-07-11

This template belongs to Mathematics courseware Beijing Normal University Edition Seventh Grade Mathematics Volume 2 industry PPT template

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