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4.2 Apply Congruence and Triangles

4.2 Apply Congruence and Triangles. Hubarth Geometry. Corresponding Parts - are angles and sides that are in the same position of their respected shape. Congruent - same size and shape. Congruent. Not Congruent. Different sizes and shapes.

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4.2 Apply Congruence and Triangles

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  1. 4.2 Apply Congruence and Triangles Hubarth Geometry

  2. Corresponding Parts- are angles and sides that are in the same position of their respected shape. Congruent- same size and shape Congruent Not Congruent Different sizes and shapes Same size and shape

  3. Congruence Statements When you write a congruence statement for two polygons, always list the corresponding vertices in the same order. You can write congruence statements in more than one way. Two possible congruence statements for the triangles at the right. F A D E B C

  4. Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. Ex 1 Identifying Congruent Parts

  5. b. You know that F Q. In the diagram, DEFG SPQR. = mQ m F = (6y + x) 68 68 = 6y + 8 10 = y a. You know that FG QR. FG = QR = 2x – 4 12 16 = 2x 8 = x Ex 2 Use Properties of Congruent Figures a. Find the value of x. b. Find the value of y.

  6. If you divide the wall into orange and blue sections along JK , will the sections of the wall be the same size and shape? Explain. The diagram shows AJ CK , KD JB , and DA BC . By the Reflexive Property, JK KJ All corresponding parts are congruent, so AJKD CKJB. From the diagram, A C and D B because all right angles are congruent. Also, by the Lines Perpendicular to a Transversal Theorem, AB DC . Ex 3 Show that Figures are Congruent Then, 1 4 and 2 3 by the Alternate Interior Angles Theorem. So, all pairs of corresponding angles are congruent.

  7. E Theorem Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. F B D C A EX 4 Use the Third Angles Theorem

  8. Write a proof. STATEMENTS REASONS Ex 5 Prove that Triangles are Congruent Plan for Proof 1. Given 2. Reflexive Property of Congruence 3. Given 4. Third Angles Theorem

  9. In the diagram at the right, ABGH CDEF. 2. Find the value of x and find m H. You know that H F (4x+ 5)° = 105° 4x = 100 x = 25 Practice 1. Identify all pairs of congruent corresponding parts. 5. By the definition of congruence, what additional information is needed to know that

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