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Congruent Triangles

Congruent triangles are defined as triangles with equal corresponding angles and sides, specifically when the ratio of two corresponding sides is 1. The document outlines various types of congruence criteria, including SSS, SAS, ASA, AAS, and Hyp-S, which describe the conditions under which triangles are considered congruent. Additionally, it provides a reference for further explanations and diagrams on the topic.

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23 views4 pages

Congruent Triangles

Congruent triangles are defined as triangles with equal corresponding angles and sides, specifically when the ratio of two corresponding sides is 1. The document outlines various types of congruence criteria, including SSS, SAS, ASA, AAS, and Hyp-S, which describe the conditions under which triangles are considered congruent. Additionally, it provides a reference for further explanations and diagrams on the topic.

Uploaded by

sikandar.ceme
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Congruent Triangles

● If given two similar triangles , the ratio of two


corresponding sides is 1, then the two triangles
are known as congruent triangles.

● In other words we say two triangles are


congruent if the corresponding angles and the
corresponding sides are equal.
A X

C Z
B Y

Note that in ∆ABC and ∆XYZ


∟ABC = ∟XYZ, ∟BAC = ∟YXZ ∟ACB =∟XZY
Also ℓ AB = ℓ XY, ℓ BC= ℓ YZ and ℓ AC = ℓ XZ

Hence ∆ABC and ∆XYZare congruent.


Denoted by ∆ABC ≡ ∆XYZ.
CONGRUENT TRIANGLES ALWAYS
Type of
Sides of both the Triangle Angles of both the Triangle
Triangle

SSS All three sides are equal

2 sides are equal The included Angle


SAS is equal

ASA Included side is equal Two angles are equal

Non- included side


AAS are equal Two angles are equal

Hyp-S Hypotenuse and a side are equal Right angled triangle


Reference
For more explanations and Diagrams you can
refer
http://argyll.epsb.ca/jreed/math9/strand3/tri
angle_congruent.htm

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