"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 3

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"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 3

The triangles are equal and the sides are proportional.

1. Two angles are equal

2. The three sides are proportional

3. Both sides are proportional and the included angles are equal.

4. The two sides are proportional and the opposite angles of one side are equal.

Are two triangles similar if their two sides are proportional and the opposite angles of one of them are equal?

Known: △A´B´C´∽△ABC

In △ABC, with B as the center,

Draw an arc with the length BA as the radius and intersect AC at D.

Connect BD, then BD=BA.

Given △ABC and △A’B’C’, determine whether they are similar based on the following conditions.

(1)∠B＝∠B’＝75°, ∠C＝50°, ∠A’＝55°

(2) ∠A＝45°, AB=12cm, AC=15cm

∠A`＝45°，A`B`＝16cm，A`C`＝20cm

(3) AB=12cm, BC=15cm, AC=24cm

A`B`=16cm, B`C`=20cm, A`C`=30cm

Can you come and help them?

On a construction site, there is a steel triangle with three sides of 20cm, 50cm, and 60cm. Due to project needs, there is an urgent need to make a triangular steel frame similar to it, but there are only two steel bars in the construction site with lengths of 30cm and 50cm. , it is too late to buy raw materials, so we can only use existing raw materials as much as possible. What should we do?

summary

How to determine if two triangles are similar:

(1) Two triangles with equal angles are similar.

(2) Two triangles whose three sides correspond to proportions are similar.

(3) Two triangles with proportional sides and equal angles are similar.

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Update Time: 2024-10-06

This template belongs to Mathematics courseware Beijing Normal University eighth grade mathematics volume 2 industry PPT template

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