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

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

From DE//BC, it can be deduced that the three sides of ΔADE and ΔABC are proportional according to the proportion of parallel line segments, and because DE//BC, ∠ADE=∠B, ∠AED=∠C, ∠A is a common angle.

preliminary theorem

If a straight line parallel to one side of the triangle intersects the other two sides (or extensions of both sides) of the triangle, the resulting triangle will be similar to the original triangle.

Analysis: There are currently only two ways to prove that two triangles are similar.

One is the definition of triangle similarity (obviously the conditions are not met); the other is the preliminary theorem.

decision theorem

If the two angles of one triangle are equal to the two angles of another triangle, then the two triangles are similar. It can be simply said: the two angles are equal and the two triangles are similar.

lemma

A straight line is parallel to the third side of a triangle if its corresponding segments are proportional.

decision theorem

For any two triangles, if the two sides of one triangle are proportional to the two sides of the other triangle and the included angles are equal, then the two triangles are similar. That is, the two sides are proportional and the included angles are equal, so the two triangles are similar.

theorem

1. Two right triangles are similar if one of their acute angles is equal.

2. Two right triangles are similar if their two right-angled sides are proportional.

small exercise

Determine whether the two triangles are similar based on the following sets of conditions?

1. ∠A= 45, AB=12cm, AC =15cm, ∠A′= 45°, A′B′=16cm, A′C′=20cm;

2. ∠B=∠B′=75°, ∠C=50°, ∠A′=55°;

3． ∠B= ∠B′=75°, ∠A=50°, ∠A′=55°;

4. AB=12cm,AC=15cm,A′B′=16cm,A′C′=20cm

5. AB = 4cm, AC=5cm, BC=6cm, A′B′= 16cm, A′C′= 20cm, B′C′= 24cm;

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"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...

"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: 2024-09-30

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