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SIMILAR TRIANGLES.

Published by Amanda Laurel Douglas Modified over 9 years ago

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Presentation on theme: "SIMILAR TRIANGLES."— Presentation transcript:

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Geometry: Similar Triangles - PowerPoint PPT Presentation

Geometry: Similar Triangles

Geometry: similar triangles ma.912.g.2.6 use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the ... – powerpoint ppt presentation.

• Review of definitions, properties and theorems of congruent and similar triangles
• Rotation ex1.ggb
• Reflection about a line ex2.ggb
• Translation by vector ex3.ggb
• Scaling ex4.ggb
• If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent.
• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.
• If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent.
• If two angles and a non included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the two triangles are congruent.
• If the hypotenuse and the leg of one right triangle are congruent to the corresponding parts of the second right triangle, the two triangles are congruent
• Similar triangles have the same shape, but the size may be different.
• Two triangles are similar if
• two pairs of corresponding angles are congruent (therefore the third pair of corresponding angles are also congruent).
• the three pairs of corresponding sides are proportional.
• To find out if triangles given in coordinate geometry are similar you can check any of the properties using coordinate geometry like distance formula
• Use graphic paper for Question 1 in handout
• Discuss in groups how you can teach topics in this section using web-based educational resources designed to reinforce learning ?
• Identify effective strategies for teaching
• Share your ideas in class discussion
• Answer the Question 2

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Similar Shapes & Triangles (Similarity) - Maths GCSE PowerPoint & ActivInspire Lesson

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

28 July 2023

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This is a maths GCSE foundation lesson on similar shapes and triangles (grade 5).

Lesson covers: scale factors, how to tell if triangles are similar and finding missing side lengths.

Includes examples, mini whiteboard section, one task and a challenge task.

PowerPoint & ActivInspire formats included.

Take back hours of your time and still deliver an excellent lesson!

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• Engage a love of learning by discussion of how the maths applies in real life
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• Mini White Board section to check for understanding - change to a “mini quiz” if no white boards available in classroom
• Lessons are scaffolded to reach all learners; gradually increase in difficulty
• Solutions for every question
• Lesson slides kept simple to prevent cognitive overload

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SIMILAR TRIANGLES

Mar 19, 2019

140 likes | 257 Views

SIMILAR TRIANGLES. Congruency. Two shapes are congruent if one of the shapes fits exactly on top of the other shape. These three triangles are all congruent. In congruent shapes: corresponding angles are equal corresponding lengths are equal.

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Presentation Transcript

Congruency Two shapes are congruent if one of the shapes fits exactly on top of the other shape. These three triangles are all congruent • In congruent shapes: • corresponding angles are equal • corresponding lengths are equal

To prove that two triangles are congruent you must show that they satisfy one of the following four sets of conditions: SSS: three sides are equal SAS: two sides and the included angle are the same ASA: two angles and the included side are the same RHS: right-angled triangle with hypotenuse and one other side the same

Which triangles are congruent to triangle A? A

Similar shapes R These two quadrilaterals are similar. S C D • In similar shapes: • corresponding angles are equal • corresponding sides are in the same ratio B A P Q To show that two triangles are similar it is sufficient to show that just one of the above conditions is satisfied.

Which triangles are similar to triangle A? A

Examples 1 The triangles are similar. Find the values of x and y. (All lengths are in cm.) 5.5 y x 8 9 Using ratio of corresponding sides: 12

Examples 2 The triangles are similar. Find the values of x and y. (All lengths are in cm.) y 7 Turn one of the triangles so that you can see which are the corresponding sides. x 12 15 8 7 Using ratio of corresponding sides:

Examples 3 Find the values of x and y. (All lengths are in cm.) x 6 Separate the two triangles. 9 2.5 2 Using ratio of corresponding sides: y x +2.5 8 y x 6 9

6 Examples 4 Find the values of x and y. (All lengths are in cm.) 4 y x 6 Turn the top triangle so that you can see which are the corresponding sides. 9 Using ratio of corresponding sides: y 4 6 x 6 9

x Examples 5 Find the values of x and y. (All lengths are in cm.) 6 12 y 16 Turn the top triangle so that you can see which are the corresponding sides. 20 Using ratio of corresponding sides: 6 12 x y 16 20

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