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4.1 Congruent Polygons. Naming & Comparing Polygons ♥List vertices in order, either clockwise or counterclockwise. ♥When comparing 2 polygons, begin at.

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Presentation on theme: "4.1 Congruent Polygons. Naming & Comparing Polygons ♥List vertices in order, either clockwise or counterclockwise. ♥When comparing 2 polygons, begin at."— Presentation transcript:

1 4.1 Congruent Polygons

2 Naming & Comparing Polygons ♥List 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. A D C B E DCBAE P I J K H IJKPH { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/4330301/14/images/slide_1.jpg", "name": "Naming & Comparing Polygons ♥List vertices in order, either clockwise or counterclockwise.", "description": "♥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. A D C B E DCBAE P I J K H IJKPH

3 Name corresponding parts Name all the angles that correspond: A D C B E P I J K H < D corresponds to < I < C corresponds to < J < B corresponds to < K < A corresponds to < P < E corresponds to < H DCBAEIJKPH Name all the segments that correspond: DC corresponds to IJ CB corresponds to JK BA corresponds to KP AE corresponds to PH ED corresponds to HI How many corresponding angles are there? How many corresponding sides are there? 55

4 How many ways can you name pentagon DCBAE? A D C B E 10 Do it. DCBAE CBAED BAEDC AEDCB EDCBA Pick a vertex and go clockwisePick a vertex and go counterclockwise DEABC CDEAB BCDEA ABCDE EABCD

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. G H F E C D B A CONGRUENCE STATEMENT ABCD = EFGH ~

7 Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent A X B C Y Z If { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/4330301/14/images/slide_6.jpg", "name": "Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent A X B C Y Z If

8 Statements Reasons XY = XL LM = YM XM = XM < L = < Y < XMY = < XML { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/4330301/14/images/slide_7.jpg", "name": "Statements Reasons XY = XL LM = YM XM = XM < L = < Y < XMY = < XML

9 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  bisect each other. StatementsReasons 1) AD and BE bisect each other. AB  DE,  A   D 1) Given 2) AC  CD, BC  CE 2) 3)  ACB   DCE 3) 4)  B   E 4) 5)  ACB   DCE 5) Given: and  A   D Prove:  ACB   DCE

12 Assignment 4.1 Reteach Worksheet 4.1 Practice Worksheet


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