2 Naming FiguresTo name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.In a congruence statement, the order of the vertices indicates the corresponding parts.
3 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.DCBAEPIJKHD corresponds to IAE corresponds to PHIJKPH
4 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
5 How many ways can you name pentagon DCBAE? 10Do it.Pick a vertex and go clockwisePick a vertex and go counterclockwiseDEABCCDEABBCDEAABCDEEABCDDCBAECBAEDBAEDCAEDCBEDCBA
6 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.
7 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~
9 Helpful HintWhen you write a statement such as ABC DEF, you are also stating which parts are congruent.
10 Naming Congruent corresponding Parts Given: ∆PQR ∆STWIdentify all pairs of corresponding congruent parts.Angles: P __, Q __, R __STWSides: PQ __, QR __, PR __STTWSW
11 More Practice1. ∆ABC ∆JKL and AB = 2x JK = 4x – 50. Find x and AB.Given that polygon MNOP polygon QRST, identify the congruent corresponding part.2. NO ____ T ____4. ∆ABC ∆EDCA __, AB __ B __, BC __C __, AC __31, 74RSPEEDDDCCEC
12 Similar PolygonsCorresponding parts must also be written in order for similar polygons.Following the order of the statement allows you to set up proportions to solve for missing parts.
13 What do you notice about the sides of the above triangles? PracticeWhat do you notice about the sides of the above triangles?
14 The “ ~ ” is used to show similarity More Similar PolygonsCorrespondence between two polygonsCorresponding angles are congruentLengths of the sides of the polygon are proportionalThe “ ~ ” is used to show similarityList all of the pairs of the congruent angles.
15 Writing Proportions using Corresponding Parts 3016BC10DE
16 What is the scale factor? What is a scale factorIf two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor.Q6RX4Y1015WBPSWhat is the scale factor?
17 Analysis of two Similar figures Statement of proportionalityis called the scale factor
18 Example10KJQZP156MLRSQuadrilateral JKLM is similar to quadrilateral PQRS. Find the value of Z