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

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"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.

If the two sides are proportional and the angles between them are equal, the two triangles are similar.

Known: As shown in the figure, ∠ABD=∠C, AD=2, AC=8, find AB.

Solution: ∵ ∠ A= ∠ A,∠ABD=∠C,

∴ △ABD ∽ △ACB ,

∴ AB : AC=AD : AB,

∴ AB2 = AD · AC.

∵ AD=2, AC=8,

∴ AB =4.

draw a picture

Draw a triangle at will, and then draw another triangle so that the length of each side is k times the length of each side of the original triangle. Measure the corresponding angles of the two triangles. Are they equal? Are these two triangles similar? Communicate with your deskmates to see if you come to the same conclusion.

As shown in the figure, in the square ABCD, point M is any point on the BC side. Connect AM and rotate the line segment AM 90° clockwise around M to get the line segment MN. Take point P on the CD side to make CP=BM and connect NP. B.P.

(1) Verify: the quadrilateral BMNP is a parallelogram;

(2) Line segments MN and CD intersect at point Q and connect AQ. If △MCQ∽△AMQ, what is the quantitative relationship between BM and MC? Please explain the reason.

As shown in the figure, in Rt△ABC, ∠ACB=90°, AC=6cm, BC=8cm. The moving point P starts from point B and moves towards point A at a speed of 5cm per second on the edge of BA. At the same time, the moving point Q Starting from point C, move towards point B at a constant speed of 4cm per second on the edge of CB. The movement time is t seconds (0＜t＜2). Connect PQ.

(1) If △BPQ is similar to △ABC, find the value of t;

(2) Connect AQ and CP. If AQ⊥CP, find the value of t;

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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" Similar PPT courseware of graphics:

"Proof of Similar Triangle Determination Theorem" Similarity of Figures PPT Courseware Learning Objectives 1. Master the proofs of the three determination theorems that two triangles are similar: two triangles whose two angles are equal are similar, two triangles whose two sides are proportional and their included angles are equal Triangles are similar, with three sides...

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Update Time: 2024-10-02

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

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