2 Naming & Comparing Polygons DCBEList vertices in order, either clockwise or counterclockwise.When comparing 2 polygons, begin at corresponding vertices; name the vertices in order and; go in the same direction.By doing this you can identify corresponding parts.DCBAEPIJKH<D corresponds to < IAE corresponds to PHIJKPH
3 Name corresponding parts Name all the angles that correspond:PIJKHADCBE< D corresponds to < I< C corresponds to < J< B corresponds to < K< A corresponds to < P< E corresponds to < HDCBAEIJKPHName all the segments that correspond:How many corresponding sides are there?DC corresponds to IJCB corresponds to JKBA corresponds to KPAE corresponds to PHED corresponds to HIHow many corresponding angles are there?55
4 How many ways can you name pentagon DCBAE? 10Do it.Pick a vertex and go clockwisePick a vertex and go counterclockwiseDEABCCDEABBCDEAABCDEEABCDDCBAECBAEDBAEDCAEDCBEDCBA
5 Polygon Congruence Postulate If each pair of corresponding angles is congruent, and each pair of corresponding sides is congruent, then the two polygons are congruent.
6 Congruence Statements Given: These polygons are congruent.Remember, if they are congruent, they are EXACTLY the same.That means that all of the corresponding angles are congruent and all of the corresponding sides are congruent.DO NOT say that ‘all the sides are congruent” and “all the angles are congruent”, because they are not.CDBAGHFECONGRUENCE STATEMENTABCD = EFGH~
7 Third Angles TheoremIf two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruentXAIf<A = <Xand<B = <Y,then<C = <ZYBZC
8 ~ Prove: ΔLXM = ΔYXM You are given this graphic and statement. Write a 2 column proof.X~Prove: ΔLXM = ΔYXMStatements ReasonsXY = XLLM = YMXM = XM< L = < Y< XMY = < XML<LXM = < YXMΔLXM = ΔYXM~Given~Given~Reflexive Property~GivenLY~MAll right angles are congruent~Third Angle TheoremPolygon Congruence Postulate~
9 Each pair of polygons is congruent Each pair of polygons is congruent. Find the measures of the numbered angles.m<1 = 110◦m<2 = 120◦m<5 = 140◦m<6 = 90◦m<8 = 90◦m<7 = 40◦
10 A student says she can use the information in the figure to prove ACB ACD. Is she correct? Explain.
11 Definition of a bisector Given:bisect each other.andA DProve: ACB DCEStatementsReasons1) AD and BE bisect each other.AB DE, A D1) Given2) AC CD , BC CE2)3) ACB DCE3)4) B E4)5) ACB DCE5)Definition of a bisectorVertical angles are congruentThird Angles TheoremPolygon CongruencePostulate
12 Assignment4.1 Reteach Worksheet4.1 Practice Worksheet