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## Similar Triangles/Polygons

Published by Maurice Conley Modified over 9 years ago

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## Presentation on theme: "Similar Triangles/Polygons"— Presentation transcript:

Ratios, Proportions, AND Similar Figures

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## Similar Shapes Triangles PPT

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

10 February 2022

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A PowerPoint lesson on Similar Shapes (Triangles) aimed at KS3-KS4 (GCSE/iGCSE). Tasks/Worksheets included within the PowerPoint

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## Similar Triangles - PowerPoint PPT Presentation

## Similar Triangles

Similar triangles similar shapes are enlargements of each other corresponding angles are equal sides are related by the same scale factor similar triangles 50 50 ... – powerpoint ppt presentation.

- Are Enlargements of each other
- Corresponding angles are equal
- Sides are related by the same scale factor
- To calculate missing sides, we first of all need the scale factor
- We then either multiply or divide by the scale factor
- To show that 2 shapes are similar we can either show that all of the sides are connected by the scale factor or show that matching angles are the same

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## Similar Triangles

Oct 31, 2013

230 likes | 670 Views

Similar Triangles. Area & Volume Scale Factor OCR Module 9. D J Millward 2008. MENU. Stage 7 Recap. AREA. VOLUME. Similar shapes. FROM STAGE 7. Are Enlargements of each other Corresponding angles are equal Sides are related by the same scale factor. Similar Triangles.

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## Presentation Transcript

Similar Triangles Area & Volume Scale Factor OCR Module 9 D J Millward 2008

MENU Stage 7 Recap AREA VOLUME

Similar shapes FROM STAGE 7 • Are Enlargements of each other • Corresponding angles are equal • Sides are related by the same scale factor

Similar Triangles Triangles are similar if matching angles remain the same size. 100º 30º 50º 100º 30º 50º

To calculate a length 5 15 5 4 x 3 x 3 6 Scale factor 3 15 12 1 3 18 Scale factor 1/3

A D E C B Harder example 3 4 6 Triangle ABC is similar to triangle ADE. DE is parallel to BC. Calculate the length of BC

3 E D 4 Harder example A 9 6 C 12 B 9 3 x 3

…and then… AB & DE are parallel Explain why ABC is similar to CDE <CED = <BAC Alternate Angles 5 A B <EDC = <ABC Alternate Angles <ECD = <ACB Vert Opp Angles 3 C 6 E D ? Triangle ABC is similar to Triangle CDE

…and then… Calculate the length of DE AC corresponds to CE Scale Factor = 2 5 A B AB corresponds to DE DE = 2 x AB 3 C DE = 10cm 6 E D ?

Summary – Similar shapes • To calculate missing sides, we first of all need the scale factor • We then either multiply or divide by the scale factor • To show that 2 shapes are similar we can either show that all of the sides are connected by the scale factor or show that matching angles are the same

AREA SCALE FACTOR 2cm 10cm² 5cm ENLARGE rectangle Scale Factor 2 40cm² 4 cm 10 cm AREA SCALE FACTOR = 4

AREA SCALE FACTOR 2cm 10cm² 5cm ENLARGE rectangle Scale Factor 3 90cm² 6 cm 15 cm AREA SCALE FACTOR = 9

AREA SCALE FACTORS • Reflect the Length Scale Factor 2² 3² AREA SCALE FACTOR = LENGTH SCALE FACTOR SQUARED ASF = LSF²

Example Questions - AREA Calculate the unknown areas Q1 Q2 5 cm 10 cm² 40 cm² 4 cm 12 cm² 8 cm Q3 15 cm 9 cm² 4 cm² 108 cm² 2 cm 3 cm

Example Questions - SIDES Calculate the unknown lengths Q1 Q2 3 cm 10 cm² 250 cm² 2 cm 12 cm² y 10 cm Q3 6 cm x 18 cm² 8 cm² 48 cm² 2 cm 3 cm z

VOLUME SCALE FACTOR 1 cm 3 cm 6 cm³ 162 cm³ 2 cm 3 cm ENLARGE cuboid Scale Factor 3 6 cm 9 cm = 3³ VOLUME SCALE FACTOR = 27

VOLUME SCALE FACTOR 4 cm 8 cm³ 8 cm 64cm³ ENLARGE cylinder Scale Factor 2 Volume Scale Factor = 2³ VOLUME SCALE FACTOR = LENGTH SCALE FACTOR CUBED VSF = LSF³

Example Questions - VOLUME Q2 Q1 2 cm 5 cm³ 8 cm³ 3 cm 27 cm³ 4.5 cm 135 cm³ 6 cm Q3 40 cm³ 5 cm³ 4 cm 2 cm

Example Questions - SIDES Q2 Q1 2 cm 5 cm³ 6 cm³ 1.5 cm 384 cm³ a 4 cm 6 cm b 40 cm³ Q3 120 cm³ 15 cm³ 3.6 cm 1.8 cm c

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## SIMILAR TRIANGLES

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SIMILAR TRIANGLES. LESSON 18(2). SIMILAR TRIANGLES. Similar is a mathematical word meaning the same shape. We say that two triangles , triangle FDE and triangle LMK, are similar if the ratio of each side is similar. FD : DE : EF = LM : MK : KL. SIMILAR TRIANGLES.

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## Similar triangles

If I take a triangle that is 3cm x 4cm x 5cm and hold it in front of a light. I can project a much larger image on a distant wall 3m x 4m x 5m These triangle are similar, so their measurements are proportional. Similar triangles.

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## Similar triangles ?

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## IMAGES

## VIDEO

## COMMENTS

Presentation Transcript. SIMILAR TRIANGLES Similar is a mathematical word meaning the same shape. We say that two triangles , triangle FDE and triangle LMK, are similar if the ratio of each side is similar. FD : DE : EF = LM : MK : KL. SIMILAR TRIANGLES This equation of two three term ratios can also be written in fraction form: FD LM DE MK EF ...

Similar Triangles. Similar shapes Are Enlargements of each other Corresponding angles are equal Sides are related by the same scale factor Similar Triangles 50º 50º 30º 30º 100º 100º Triangles are similar if matching angles remain the same size. Show that these triangles are similar 50º 50º 10º 10º 120º 120º To calculate a length 4 ...

In the triangles below, the corresponding sides are the ones that are connecting the corresponding angles. They are in proportion to each other and have the same relative position. So, ~ and ~ and ML ~. 8 Corresponding sides In similar triangles, corresponding sides are proportional. That means that they have been either enlarged or reduced by ...

Similar Triangles. 25. 1. Identify properties of similar triangles. 2. Calculate the value of missing side lengths of similar triangles. 3. Apply ratios to similar triangles. LEARNING TARGETS <Learning.Targets> Chapter #: ... PowerPoint Presentation Subject: Math Last modified by:

Presentation Transcript. triangle angle degree congruent similar Fast Facts The sum of its interior angles is 180°. H K J L I G AA Similarity • If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Two corresponding angles are congruent.

Similar Triangles PPT and examples - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. The document discusses proportional relationships and similar triangles. Some key points: - Triangles are similar if corresponding angles are congruent and corresponding sides are proportional.

Side-Angle-Side (SAS) Similarity Theorem - If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles must be similar. (This is like SAS congruency) 𝟐𝟕𝟏𝟖 = 𝟑𝟔𝟐𝟒= 𝟏.𝟓

KS3/KS4 Maths Similar Triangles. Subject: Mathematics. Age range: 11-14. Resource type: Other. File previews. pptx, 926.67 KB. PPT looking at how to identify similar triangles and find missing lengths. Tes classic free licence.

Download ppt "SIMILAR TRIANGLES." Similar presentations . Proving Triangles Congruent. By: THE "A" SQUAD (Annie and Andrew) SIMILAR TRIANGLES. Blue - 3/9/2015 Gold - 3/10/2015. Last 2 classes, we talked about 3 ways we can determine triangle congruence. CPCTC - All 3 sides and 3 angles of.

Presentation Transcript. Triangle Similarity Keystone Geometry. F C A B D E Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. Similar Polygons ~ means "is similar to". Congruence vs. Similarity • If two triangles are congruent, then they are ...

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When two triangles are equiangular, then one triangle is an enlargement of the other - they are known as similar triangles. Their sides will be proportion, that is, the ratio of the lengths of the same sides is the same. 𝑋𝑌 𝐴𝐵 = 𝑌𝑍 𝐵𝐶. Here are some common examples of similar triangles. Note the parallel sides in the ...

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SIMILAR TRIANGLES. Identify similar triangles Use similar triangles to solve problems. Eiffel Tower. POSTULATE Angle-Angle (AA) Similarity. If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Example:. THEOREM. 272 views • 9 slides

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SIMILAR TRIANGLES. Identify similar triangles Use similar triangles to solve problems. Eiffel Tower. POSTULATE Angle-Angle (AA) Similarity. If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Example:. THEOREM. 269 views • 9 slides

Similar Triangles. Area & Volume Scale Factor OCR Module 9. D J Millward 2008. MENU. Stage 7 Recap. AREA. VOLUME. Similar shapes. FROM STAGE 7. Are Enlargements of each other Corresponding angles are equal Sides are related by the same scale factor. Similar Triangles.