Geogebra Warm-up Open a 5.3 geogebra file on scevmath.org.

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Proving Triangles Congruent

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Presentation transcript:

Geogebra Warm-up Open a 5.3 geogebra file on scevmath.org. Construct two triangles with the given angles and/or side lengths. Find the measures of the remaining angles by using the angle tool. Find the side lengths by right clicking on the side, clicking ‘object properties’, then ‘show label, value’. See if your triangles are (close to) congruent. See if your partner’s triangles are congruent.

Congruence Two triangle are congruent if and only if all the corresponding angles and sides are congruent.

SSS If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.

A D C B

SAS If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

AAS If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent.

T A C O S

SSA Bad word = Bad conjecture

HL If the hypotenuse and the leg of one triangle are congruent to the hypotenuse and leg of another triangle, then the triangles are congruent.

I P D O

Corresponding Parts in Congruent Triangles are CPCTC Corresponding Parts in Congruent Triangles are

Prove

tell me everything you know… So…. Knowing that there are congruent triangles tells us A LOT OF INFORMATION tell me everything you know…