# Lecture 4.3

Kristoffer Brown
13 de Jan de 2010
1 de 17

### Lecture 4.3

• 1. Geometry - 4.3 Congruent Triangles
• 2. Congruent, Corresponding Angles/Sides Two figures are congruent when their corresponding sides and corresponding angles are congruent. Corresponding Angles Corresponding Sides There is more than one way to write a congruence statement, but the you must list the corresponding angles in the same order.
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• 4. Naming Congruent Parts Write a congruence statement for the triangles below. Identify all pairs of congruent parts. Corresponding Angles Corresponding Sides
• 5. Identify Corresponding Congruent Parts Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE  RTPSQ . Sides: Angles:
• 6. Third Angle Thm Third Angle Thm. - If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If and then,
• 7. Properties of Congruent Triangles Transitive Property of Congruent Triangles Reflexive Property of Congruent Triangles Symmetric Property of Congruent Triangles
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• 10. Using the Third Angle Thm. Find the value of x.
• 11. Determining Triangle Congruency Decide whether the triangles are congruent. Justify your reasoning. From the diagram all corresponding sides are congruent and that <F and <H are congruent. <EGF and <HGJ are congruent because of Vertical angles. <E and <J are congruent because of the third angle theorem Since all of the corresponding sides and angles are congruent,
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• 13. Use Corresponding Parts of Congruent Triangles In the diagram, Δ ITP  Δ NGO . Find the values of x and y .  O   P 6 y – 14 = 40 6 y = 54 y = 9 x – 2 y = 7.5 x – 2(9) = 7.5 x – 18 = 7.5 x = 25.5 Answer: x = 25.5, y = 9
• 14. A. x = 4.5, y = 2.75 B. x = 2.75, y = 4.5 C. x = 1.8, y = 19 D. x = 4.5, y = 5.5 In the diagram, Δ FHJ  Δ HFG . Find the values of x and y .
• 15. Proof: Prove: Δ LMN  Δ PON 2.  LNM   PNO 2. Vertical Angles Theorem Statements Reasons 3.  M   O 3. Third Angles Theorem 4. Δ LMN  Δ PON 4. Def of Congruent Triangles 1. Given 1.
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