Bell Work 12/12 State which two triangles, if any, are congruent, and write a congruence statement and reason why 1) 2) Solve for the variables 3) 4)

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Presentation transcript:

Bell Work 12/12 State which two triangles, if any, are congruent, and write a congruence statement and reason why 1) 2) Solve for the variables 3) 4)

Outcomes I will be able to: 1) Prove triangles are congruent by SSS, SAS, ASA, AAS by writing proofs 2) Use Triangle Sum Theorem, Exterior Angle Theorem, and prove triangle congruence

Coordinate Proofs Using Geometry Pad and looking at triangles in the coordinate plane, we can prove triangles are congruent. See overhead for 1st example. ***You will be able to prove the triangles using whichever congruence postulate you would like, as long as you provide valid reasoning.

Review Side-Side-Side: All three pairs of sides in each triangle must be congruent to the sides in the other Side-Side-Side: s Congruence Statement ***Be sure corresponding parts line up in congruence statement ***If it helps actually write what pieces are congruent!!!

Review Side-Angle-Side: Two pairs of sides and the angle between them must be congruent Side-Angle-Side: ***Start at a side and move to the next closest piece that is marked to determine which congruence postulate to use

Review Which pair of triangles below uses SAS? Can we prove triangle congruence in any of the others? Pair 4

Review Angle-Side-Angle- Two pairs of angles and the side between them must be congruent Angle-Side-Angle-

Review Which pair of triangles makes use of the ASA congruence postulate?

Review Angle-Angle-Side: Two pairs of angles and a side next to one of the angles must be congruent Angle-Angle-Side:

Review Identify Which pair does not show AAS. Which congruence statement does it show?

Triangle Sum Triangle Sum Theorem states: All three angles in a triangle must add to 180° How do we find x? 67 + 43 + x = 180 110 + x = 180 x = 70

Exterior Angle Theorem Exterior Angle Theorem states: That an angle exterior to a triangle is equal to the sum of the two nonadjacent interior angles How do we find x? 80 + 40 = x 120° = x

Base Angle Theorem Base Angle Theorem states: The base angles in an isosceles triangle are congruent How do we find x? x = 46° b/c base angles are congruent How do we find y? 46 + 46 + y = 180 92 + y = 180 y = 88°

Hypotenuse-Leg ***Hypotenuse-Leg may only be used in right triangles. It states: As long as the hypotenuse and the leg of two right triangles are congruent, then the triangles are congruent Are these triangles congruent? Yes, the hypotenuse and a leg are congruent.

Proofs Your table will be given 6 different proofs. You need to prove that each of the six triangles are congruent by using the congruence postulates You have 20 minutes to complete this task Be sure to check your proof with another group because 6 pairs will be ask to explain the proofs on the board ***There will be at least 2 proofs on the Quizzam Friday(you will be able to use your notes).