"Similar Triangles" Similar PPT Courseware 2

Description

"Similar Triangles" Similar PPT Courseware 2

Review and Reflection

How to determine if two triangles are similar:

1. Definition: Two triangles whose corresponding triangles are equal and whose three sides are proportional are similar.

2. When the straight line on one side of a parallel triangle intersects the other two sides (or the extension lines of both sides), the triangle formed is similar to the original triangle.

3. Two triangles are similar if the three sides correspond to proportions.

4. Two triangles with proportional sides and equal angles are similar.

5. Two triangles with equal angles are similar.

Properties of similar triangles:

1. Corresponding angles of similar triangles are equal and corresponding sides are proportional.

2. Similar triangles correspond to the height line ratio, the corresponding midline ratio, and the corresponding angle bisector ratio equal to the similarity ratio.

3. The perimeter ratio of similar triangles is equal to the similarity ratio, and the area ratio is equal to the square of the similarity ratio.

When ∠BCF = ∠A, �BCF∽ �BAC.

(1) If BC=6, AF=5, can you find the length of BF?

(2) BC is the tangent line of circle O, and the tangent point is C.

(3) If point A is moved so that AC becomes the diameter of ⊙O, what other conclusions can you draw?

Use it once

(1) Please find a point D on the x-axis such that �BDA is similar to �BAC (excluding congruence), and find the coordinates of point D;

(2) Under the condition of (1), if P and Q are moving points on BA and BD respectively, connect PQ and assume BP=DQ=m,

Question: Is there such a m that makes �BPQ similar to �BDA? If it exists, request the value of m; if it does not exist, please explain the reason.

question:

As shown in the figure, in square ABCD, E is any point on BC (not coincident with B and C) ∠AEF=90°. Observe the graph:

(1) Are △ABE and △ECF similar? and justify your conclusion.

(2) If E is the midpoint of BC and connects AF, what similar triangles are there in the picture?

Practical exercises and application of knowledge

Variation: In the right-angled trapezoid ABCF, ∠B=90°, CB=14, CF=4, AB=6, CF∥AB, find a point E on the side CB to make a triangle with E, A, and B as vertices. Similar to the triangle with E, C, and F as vertices, then CE=_______

1. In the rectangle ABCD, fold DA in half along AF so that D coincides with the point E on the edge of CB. If AD=10, AB= 8, then EF=______

2. It is known that: D is a point on BC, ∠B= ∠C= ∠EDF=60°, BE=6, CD=3, CF=4, then AF=_______

Keywords: Similar teaching courseware, similar triangle teaching courseware, New People's Education Edition ninth grade mathematics volume 2 PPT courseware, ninth grade mathematics slide courseware download, similar PPT courseware download, similar triangle PPT courseware download, .ppt format

For more information about the "Similar Triangles Are Similar" PPT courseware, please click the Similar Triangles ppt Similar ppt tag.

"Properties of Similar Triangles" PPT Courseware 3:

"Properties of Similar Triangles" PPT Courseware 3 Situation Introduction: Known: ABC∽A'B'C', according to the definition of similarity, what conclusions do we have? Viewed from corresponding sides: __________________ Viewed from corresponding angles: __________________ Two triangles..

"Properties of Similar Triangles" PPT Courseware 2:

"Properties of Similar Triangles" PPT Courseware 2 1. The ratios of the corresponding heights, the ratios of the corresponding midlines, and the ratios of the corresponding angle bisectors of similar triangles are all equal to ________. 2. The ratio of the perimeters of similar triangles is _________. 3． The ratio of the areas of similar triangles is equal to______..

"Determination of Similar Triangles" PPT Courseware 3:

"Determination of Similar Triangles" PPT Courseware 3 1. Three sides correspond to two proportional triangles ________. When using this judgment method to prove that two triangles are similar, pay attention to the corresponding relationship. Generally speaking, the opposite sides of equal angles are ________ sides. 2. Right triangle...

File Info

Update Time: 2024-11-22

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 2 industry PPT template

Preview