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Transcript
Unit 1B2 Day 2 Do now Tell whether it is possible to create each of the following: acute scalene triangle obtuse equilateral triangle right isosceles triangle scalene equiangular triangle right scalene triangle Congruence Informal: Two figures are congruent if they have exactly the same size and shapes. Two figures are congruent if and only if their corresponding parts are congruent. Definition of congruent triangles: all _________ pairs of corresponding sides congruent; all _________ pairs of corresponding angles congruent. Ex. 1: Proving Congruence Are the two triangles congruent? Use the definition of congruent triangles. If so, write a congruence statement. Ex. 1A: Congruent Figures In the diagram, NPLM ≅ EFGH. Find the values of x and y. Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then ______________________ __________________________________ Ex. 2: Third Angles Theorem Find the value of x. Ex. 2A In the diagram, ABCD ≅ KJHL. Find the values of x and y. Ex. 3: Determining Congruence Determine whether the triangles are congruent. Justify your reasoning. Ex. 3A Decide whether the triangles are congruent. Justify your reasoning. Ex. 4: Proving Congruence Given: AB || DC, AB ≅ DC, E is the midpoint of BC and AD. Prove: ΔAEB ≅ ΔDEC Properties of Congruent Triangles Reflexive property of congruent triangles: Every triangle is congruent to ____________. Symmetric property of congruent triangles: If ΔABC ≅ ΔDEF, then _________________ Transitive property of congruent triangles: If ΔABC ≅ ΔDEF and ΔDEF ≅ ΔJKL, then ______________. Closure If ΔGHJ ≅ ΔMNP, what corresponding angles and sides are congruent?