"Determination of Similar Triangles" PPT Courseware 3

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"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. How to determine the similarity of right triangles:

Two right triangles with equal acute angles are similar;

Two right-angled sides correspond to two proportional right-angled triangles that are similar;

Two right triangles whose hypotenuse and right-angled sides are proportional are similar.

1. (4 points) The lengths of the three sides of △ABC are 6, 8, and 12 respectively, the lengths of the three sides of △A1B1C1 are 2, 3, and 2.5 respectively, and the lengths of the three sides of △A2B2C2 are 6, 3, and 4 respectively.

Then △ABC is similar to ________.

2. (4 points) If △ABC and △DEF satisfy the following conditions, what makes △ABC and △DEF similar is ()

A． AB=6, BC=6, AC=9, DE=4, EF=4, DF=6

B． AB=4, BC=6, AC=8, DE=5, EF=10, DF=15

C. AB=1, BC=√2, AC=2, DE=√6, EF=√3, DF=√5

D. AB=1, BC=√5, AC=3, DE=√15, EF=√23, DF=√6

1. Multiple choice questions (7 points in total)

10. Among the following conditions, the ones that can determine △ABC∽△A′B′C′ are ()

①∠A=45°, AB=24, AC=30, ∠A′=45°, A′B′=32, A′C′=40;

②AB=6, BC=7.5, AC=12, A′B′=10, B′C′=12.5, A′C′=20;

③∠A=47°, AB=1.5, AC=2, ∠A′=47°, A′B′=2.8, B′C′=2.1.

A． 0 B． 1

C. 2 D. 3

【Integrated use】

15. (14 points) The side lengths of a steel tripod are 20 cm, 50 cm, and 60 cm respectively. Now we want to make a steel tripod similar to it, but there are only two steel bars with lengths of 30 cm and 50 cm. It is required to use one of them. The root is one side, and two sections are cut from the other root (remaining material is allowed) as both sides. How many different cutting methods are there?

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"Determination of Similar Triangles" PPT Courseware 2:

"Determination of Similar Triangles" PPT Courseware 2 The two sides correspond to two triangles that are proportional and have equal angles _________. This determination method can be understood by analogy with SAS in congruent triangles. The two conditions of this theorem involve angles and sides respectively. Both are indispensable, and this...

"Determination of Similar Triangles" PPT courseware:

"Determination of Similar Triangles" PPT courseware 1. If the angles of two triangles are equal, then the two triangles ________. 2. It is a common method to prove that two triangles are similar through the equality of two angles. The key to its application is to find the ________ angle. Generally speaking...

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Update Time: 2024-11-23

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 1 industry PPT template

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