"Proof of Similar Triangle Determination Theorem" Similarity PPT Courseware of Figures

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"Proof of Similar Triangle Determination Theorem" Similarity PPT Courseware of Figures

learning target

1. Master the proofs of the three determination theorems that two triangles are similar: two triangles with two equal angles are similar, two triangles with two sides that are proportional and the angles are equal are similar, and two triangles with three sides that are proportional are similar.

2. Be able to use the conditions of triangle similarity to solve simple practical problems, further improving students' logical reasoning ability and preliminary logical judgment ability.

1. What are congruent triangles?

2. What are the methods for determining congruent triangles?

1. What are similar triangles?

2. To satisfy six elements at the same time, it feels too complicated to determine. Do you want to find some simple methods to determine whether two triangles are similar?

As long as the shape of the triangle is determined, regardless of its size, what conditions are needed?

Can you draw a triangle similar to the one I have in the simplest way with the fewest conditions?

Option 1: Draw a △A′B′C′

Let ∠A′=∠A=60°, ∠B′=∠B=45°.

① Compare the triangles made by the same tablemates and make an intuitive judgment on the shape;

② Compare the triangle in the hands of the teacher on the physical projector;

③Guess: If the two angles are equal, it can be determined that the two triangles are similar.

New application knowledge: Line a and line b intersect at point A. Points B and C are on line a and line b respectively. Find two points D and E on line a and line b respectively to make △BAC and △DAE similar. Please Draw as many points D and E as possible.

Discuss

Is the "angle" in the above determination method necessarily the angle between two corresponding sides?

Two triangles whose sides are proportional and whose opposite angles are equal are not necessarily similar.

1. judge

(1) Two right triangles with an equal acute angle are similar. ( )

(2) Two isosceles triangles with equal angles are similar. ( )

(3) Two isosceles triangles with equal vertex angles are similar. ( )

2. There is a pond surrounded by open space. If you want to measure the distance between A and B at the two ends of the pond, can you use the knowledge you learned in this section to solve this problem?

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For more information about the PPT courseware "Proof of the Determination Theorem of Similar Triangles on the Similarity of Graphs", please click on the Proof of the Determination Theorem of Similar Triangles on the Similarity of Graphs ppt tag.

"Proof of Similar Triangle Determination Theorem" Similarity of Figures PPT Courseware 3:

"Proof of Similar Triangle Determination Theorem" Similarity of Figures PPT Courseware 3 From the fact that DE//BC is proportional according to the segmentation of parallel lines, the three sides of ADE and ABC are proportional, and because DE//BCADE=BAED=CA is public Angle. Preliminary Theorem Parallel to a side of a triangle..

"Proof of Similar Triangle Determination Theorem" Similarity of Figures PPT Courseware 2:

"Proof of Similar Triangle Determination Theorem" Similarity of Figures PPT Courseware 2 How to Determine Similar Triangles: Two angles are equal and two triangles are similar. Three sides are proportional and two triangles are similar. Two sides are proportional and the angles are equal and two triangles are similar. Known: Such as...

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Update Time: 2024-10-01

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

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