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Transcript
+ Triangle Congruences Day 2 + Warm Up (Monday) 1. Find the missing angles below y 70 x 70 2. 40 40 10 minutes Use Pythagorean Theorem to find the missing side d 4 3 End + Today’s Objective Use triangle congruence postulates and theorems to prove that triangles are congruent. + Short Activity Using the spaghetti pieces provided, create a triangle and tape it to the transparency paper. When finished, place on Ms. Samara’s desk + Proving Triangles Congruent By the definition of Congruence, what do we need to show to prove two triangles are congruent? All corresponding angles are congruent All corresponding sides are congruent That’s With six pairs! Triangles, we have postulates that allow us to only need to show three pairs, but they have to be in a specific order + If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. + If two sides and the included (between) angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. + Non-example of SAS: Why can’t we use SAS to show these triangles are congruent? + If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. + We now have the following: SSS – side, side, side SAS – Side, Angle (between), Side ASA – Angle, Side (between), Angle + Examples Which Theorem proves the Triangles are congruent? 1. + Sometimes we have to mark Assumptions! Assumption #1: Reflexive Property If two triangles share a side, that side is congruent to itself + What do we know about the third angle if two are congruent? 2. + Assumption #2: Third Angle If two pairs of corresponding angles are congruent, then the third pair is also congruent! Why? Triangle Angle Sum Theorem says the measures of the angles have to sum to 180! + What do we know about vertical angles? 3. + Assumption #3: Vertical Angles Vertical Angles are Congruent! + 4. + 5. + Assumption #4: Third Side of a RIGHT Triangle If two pairs of corresponding sides are congruent in a RIGHT TRIANGLE, then the third pair is also congruent! Why? Pythagorean Theorem states that a2+b2=c2. This can only be true if a, b, and c are the same in both triangles + Exit Ticket - Worksheet HOMEWORK - Worksheet