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Lesson Posted on 03 Jan Similarity

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

Similar figures and congruent figures both have the same shape. Two triangles are congruent if they are the same size and shape. Congruency:They are exactly same in length, width, shape, size etc. They are similar if they are the same shape (and maybe or maybe not the same size). Also remember: i. Every... read more

Similar figures and congruent figures both have the same shape.

Two triangles are congruent if they are the same size and shape.

Congruency:They are exactly same in length, width, shape, size etc.

They are similar if they are the same shape (and maybe or maybe not the same size).

Also remember:

i. Every congruent pair of shapes is similar also.

ii. Not all similar figures are congruent though.

iii. The areas of two similar figures may be different.

iv. However, the areas of two congruent figures are equal.

v. Ratio of Corresponding Sides:

a. The ratios between the corresponding sides of two similar figures are equal.

b. The ratios between the corresponding bases of two congruent figures are always one.

vi. Symbol:

a. The symbol ≅ is for Congruent.

b. The symbol ~ is for Similar.

vii. Examples:

You went to a garment store to buy shirts. You liked one with black strips. You saw they were kept in various sizes: S, M, L, XL, XXL…

Now these shirts of different sizes are similar because they have the same shape.

But 2 shirts of the same size are congruent. They are exactly same in length, width, shape, size etc.

Two triangles are said to be similar to each other when they have same shape, proportion and angles but different sizes

Congruence on the other hand means when two things are exactly identical to each other.

The difference between similar figures and congruent figures is that congruent figures also have the same size. So, corresponding sides and corresponding angles of congruent figures have the same measures.

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Comments Answered on 06/12/2016 Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Souvik Barua

Btech/BE Tutoring

The SSS rule states that:- If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. In the diagrams below, if AB = RP, BC = PQ and CA = QR, then triangle ABC is congruent to triangle RPQ. Side - Side - Side (SSS) Rule Side-Angle-Side (SAS) Rule Side-Angle-Side... read more

The SSS rule states that:- If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. In the diagrams below, if AB = RP, BC = PQ and CA = QR, then triangle ABC is congruent to triangle RPQ. Side - Side - Side (SSS) Rule Side-Angle-Side (SAS) Rule Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that :- If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent. An included angle is an angle formed by two given sides. Included and Non-included angle:- Included Angle Non-included angle For the two triangles below, if AC = PQ, BC = PR and angle C = angle P , then using the SAS rule, triangle ABC is congruent to triangle QRP congruent triangles Angle-Side-Angle (ASA) Rule Angle-side-angle is a rule used to prove whether a given set of triangles are congruent. The ASA rule states that If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent. Angle-Angle-Side (AAS) Rule Angle-angle-side is a rule used to prove whether a given set of triangles are congruent. The AAS rule states that If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent. In the diagrams below, if AC = QP, angle A = angle Q, and angle B = angle R, then triangle ABC is congruent to triangle QRP. read less

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Answers 18 Comments Answered on 30 Jan Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Sujoy D.

Tutor

There are the following steps to prove that two triangles are similar:- 1. AAA Test (angle angle angle): All three pairs of corresponding angles are the same. 2. SSS Test (side side side): All three pairs of corresponding sides are in the same proportion. 3. SAS Test (side angle side): Two pairs of sides... read more

There are the following steps to prove that two triangles are similar:- 1. AAA Test (angle angle angle): All three pairs of corresponding angles are the same. 2. SSS Test (side side side): All three pairs of corresponding sides are in the same proportion. 3. SAS Test (side angle side): Two pairs of sides are in the same proportion and the angle between them is equal.

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Answers 9 Comments Answered on 30 Jan Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Sujoy D.

Tutor

Two triangles are similar if they have: -All their angles equal. -Corresponding sides are in the same ratio.

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Answers 6 Comments Answered on 30 Jan Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Sujoy D.

Tutor

3 main criteria for similarity of triangles 1) AAA or AA 2) SSS 3) SAS.

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Answers 6 Comments Answered on 30 Jan Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Sujoy D.

Tutor

In a right angled triangle the square of the long side is equal to the sum of the squares of the other two sides. It is stated in this formula: a2 + b2 = c2

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Answers 6 Comments Answered on 27/11/2016 Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Shanta Kothari

Complementary angles are the angles which add up to 90 and supplementary angles are the angles that add up to 180 .

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Answers 6 Comments Answered on 09/12/2016 Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Define SAS axiom?

Ankit

JEE/Board Maths Tutor

If one angle between two adjacent sides of a triangle is similar to angle between two sides of another triangle then two triangles are congruent.

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Answers 4 Comments Answered on 21/11/2016 Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

What are the three conditions by which two triangles are proved similarity?

Manish V

Tutor

SSS,SAS,AA

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Answers 3 Comments Answered on 22/11/2016 Tuition/Class IX-X Tuition Tuition/Class IX-X Tuition/Mathematics Similarity

Is it possible to measure the similarities of any geometrical shapes?

Jayam Sagar

Home Tutor

Yes

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