WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides...
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Transcript of WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides...
![Page 1: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/1.jpg)
WHAT IS A CONGRUENT TRIANGLE??
![Page 2: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/2.jpg)
Definition
Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.
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What makes a triangle?
A triangle is composed of 6 parts:3 sides3 angles
If all 6 of these parts are congruent to another triangle, then we can say that the two triangles are congruent.
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Visual/Picture
![Page 5: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/5.jpg)
Order Matters!!
It is very important to remember that the order of the congruent parts of triangles matters.
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Examples/Models
![Page 7: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/7.jpg)
Non-Examples
![Page 8: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/8.jpg)
Congruent Triangle
Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.
![Page 9: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/9.jpg)
![Page 10: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/10.jpg)
Triangle Congruence
SAS, AAS, ASA, SSS, HL
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Shortcuts to congruence
Should we really need to find all 6 parts of a triangle to show they are congruent or can we use shortcuts?
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Side-Side-Side
If two triangles have ALL 3 of the same side lengths, then we can say they are congruent by the SSS postulate
side
side
side
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Side-Angle-Side
If two triangles have the same side lengths and the same angle measure in-between those sides, the two triangles are congruent by the SAS postulate.
side
angle side
![Page 14: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/14.jpg)
Angle-Side-Angle
If two triangles have 2 congruent angles and a congruent side in-between those angles, then they are congruent by the ASA postulate
angleangle
side
![Page 15: WHAT IS A CONGRUENT TRIANGLE??. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles.](https://reader036.fdocuments.us/reader036/viewer/2022082818/56649efd5503460f94c10fd9/html5/thumbnails/15.jpg)
Angle-Angle-Side
If two triangles have 2 congruent angles and a congruent side that isn’t in-between them, then the triangles are congruent by the AAS postulate
angle
angle
side
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What about Angle-Side-Side? Angle-Side-Side is not enough to
prove triangles are congruent. As an easy way to remember
that:
don’t be an and try to useA.S.S.
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Hypotenuse-Leg
If the hypotenuse and the same leg of two right triangles are congruent then the two right triangles are congruent.
hypot hypotleg leg