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Bell Work a. What appears to be true about the lengths of the three tower braces that form a triangle? b. It also appears that the three angles of the triangles formed by the braces are congruent. If this is true, what is the measure of each of the angles? c. If the braces formed noncongruent angles, could the lengths of the braces still be congruent? Why? Chapter 4 Congruent Triangles 4-1 Classifying Triangles Essential Question: How do I identify and classify triangles by angle measures and side measures? scalene triangle isosceles triangle equilateral triangle equiangular triangle acute triangle right triangle obtuse triangle Summary Homework p. 239 #16-38 even Exit p. 244 Bell Work a. What measurements other than the pivot angle must be programmed so that the robot will move in a triangular path? b. The pivot angles shown in the picture are all acute angles. Must each pivot angle be an acute angle? Why? c. Regardless of the robot's path, the sum of the measures of a the pivot angles must always be the same. What is that sum? 4-2 Angles of Triangles Essential Question: How do I apply the Triangle Angle Sum Theorem and the Exterior Angle Theorem? exterior angles - formed by one side of the triangle and the extension of an adjacent side. Remote interior angles - not adjacent to the exterior angle corollary - a statement that can easily be proven using a theorem Summary Homework p. 248 #12-32 even Exit Bell Work a. Why must the shape and size of the faceplate exactly match the space where it fits? b. What other parts of the faceplate must match the space where its fits exactly? c. What is the implication of the corresponding components of the faceplate and the car stereo not matching exactly? 4-3 Congruent Triangles Essential Questions: How do I name and use corresponding parts of congruent polygons? How do I prove triangles congruent using the definition of congruence? Definition Examples Description congruent Non-Examples Definition of Congruent Polygons Two polygons are congruent if and only if their corresponding parts are congruent. Write the congruence statements. Summary Homework p. 257 #10-22 even Exit Bell Work Bell Work Find x and y. Discovery Activity 1. Supply 2. Builder 3. Writer Exit What have you discovered about congruent triangles? Bell Work a. How is the board affected if the side arms are not the same distance from the top of the board? b. What must be true if ΔABC≅ΔXYZ? c. How is the congruence of the triangles discussed affected if the sides arms are not propositioned the same distance from the top of the boards? 4-4 Proving Triangles Congruent - SSS and SAS Essential Question: How do I use the SSS and SAS Postulates to test for triangle congruence? Summary Homework p. 267 #6, 8, 10, 12, 16-18 Exit Bell Work Write the congruent statement. 4-5 Proving Triangles Congruent -ASA, AAS Essential Question: How do I use the ASA and AAS Postulates to test for triangle congruence? Summary Homework p. 276 #1, 4, 13, 14, 15 Exit Write the congruent statement. Bell Work Bell Work Are the triangles congruent? If they are write the congruence statement and give the reason. Exit What are you going to do to study for the quiz tomorrow? Bell Work Are the triangles congruent? If they are write the congruence statement and give the reason. Exit How do you think you did on the quiz and why? Bell Work a. Why are the triangles isosceles? b. What appears to be true about the angles opposite the equal sides? c. What type of triangle results if the third side of the triangle is congruent to the other 2 sides? d. What do you think is true of the three angles if the three sides are congruent? 4-6 Isosceles and Equilateral Triangles Essential Question: How do I use properties of isosceles and equilateral triangles? Find the value of x and y. Find the value of x and y. Summary Homework p. 287 #10-24 even Exit Find the value of each variable.