Bell Work Find the value of the missing variable 1)2) 3) 4)

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Presentation transcript:

Bell Work Find the value of the missing variable 1)2) 3) 4)

OUTCOMES I will be able to: 1) Prove that triangles are congruent by SSS or SAS 2) Prove that triangles are congruent by ASA or AAS

Congruence Review What is a congruence statement for the triangles below? ***Remember, corresponding parts(congruent parts) must line up in the congruence statement.

Congruent Triangle Investigation 1) Cut out the strips at the bottom of your paper. 2) Compare your triangle to someone around you. Do you notice anything about them? 3) How can you prove this is true? 4) Plot at point at each intersection, then draw your triangle and label it ABC 5) Measure the sides and angles. Is your triangle congruent to those near you? Why?

Congruent Triangles Shortcuts Side-Side-Side Congruence Conjecture- If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent Key is to make sure corresponding parts line up Side

Example 1 Side KL is congruent to Side NM. Side LM is congruent to Side MP. Side KM is congruent to NP. Therefore, ∆KLM is congruent to ∆NMP by SSS.

4.3 Congruent Triangles Side-Angle-Side Conjecture: If two sides of two triangles are congruent and the angle between them is also congruent, then the two triangles are congruent Side Angle Side ***Look at where the angle is located!!!

Congruent Triangle Shortcut Examples Given Side-Angle-Side Always pick a spot and go in order!!! ***Always look for things that could be congruent

Congruent Triangle Shortcut Examples Given Side-Side-Side ***Always pick a spot and go in order when writing a proof

Congruent Triangles Shortcut Examples Try on your own!!! ***Remember that what is marked is given!!! Given Side-Angle-Side

Congruent Triangle Examples Try on your own!!! ***Always look to see if the triangles share anything!!! Yes, since they share PM, we can mark it as congruent

SSS Review Can we prove that the following triangles are congruent? Why or why not? A)B) Triangles aren’t congruent

4.4 Congruent Triangles Angle-Side-Angle Conjecture – If two angles and the included side of one triangle is congruent to two angles and the included side of a second triangle, then the two triangles are congruent. ***Included side is the side between the angles -Angle -Side -Angle

4.4 Congruent Triangles Angle-Angle-Side Conjecture – If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. What do we have that is congruent? - Angle - Side

Examples What do we know about Angle ACB and Angle ECD? Does this help prove triangle congruence? They are congruent because of vertical angles No, AAA does not prove congruence

Examples What do we know about Angle XWV and Angle ZWY? They are congruent, b/c of vertical angles What does that give us? Angle Side Angle

Examples What do we know about Angle C and Angle D? Why? Alternate Int Angle Angle Given Vertical Angles Given AD II CE Angle Side Angle Side Angle

Examples Always look for something that they share, and mark what we know. Given Reflexive Angle-Angle-Side If you need to, pull apart the triangles ***See board A A S