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Geometry Practice: Triangles and Congruence

Practice congruence statements, theorems, and constructions related to triangles in geometry. Learn to identify isosceles and equilateral triangles, and solve for missing measures.

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Geometry Practice: Triangles and Congruence

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  1. Splash Screen

  2. Refer to the figure. Complete the congruence statement.ΔWXY  Δ_____ by ASA. ? A.ΔVXY B.ΔVZY C.ΔWYX D.ΔZYW 5-Minute Check 1

  3. Refer to the figure. Complete the congruence statement. ΔWYZ  Δ_____ by AAS. ? A.ΔVYX B.ΔZYW C.ΔZYV D.ΔWYZ 5-Minute Check 2

  4. Refer to the figure. Complete the congruence statement. ΔVWZ  Δ_____ by SSS. ? A.ΔWXZ B.ΔVWX C.ΔWVX D.ΔYVX 5-Minute Check 3

  5. What congruence statement is needed to use AAS to prove ΔCAT ΔDOG? A. C  D B. A  O C. A  G D. T  G 5-Minute Check 4

  6. Content Standards G.CO.10 Prove theorems about triangles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. CCSS

  7. You identified isosceles and equilateral triangles. • Use properties of isosceles triangles. • Use properties of equilateral triangles. Then/Now

  8. legs of an isosceles triangle • vertex angle • base angles Vocabulary

  9. Concept

  10. ___ BCA is opposite BA and A is opposite BC, so BCA  A. ___ Congruent Segments and Angles A. Name two unmarked congruent angles. Example 1

  11. ___ BC is opposite D and BD is opposite BCD, so BC  BD. ___ ___ ___ ___ Congruent Segments and Angles B. Name two unmarked congruent segments. Example 1

  12. A. Which statement correctly names two congruent angles? A.PJM PMJ B.JMK JKM C.KJP JKP D.PML PLK Example 1a

  13. A.JP PL B.PM PJ C.JK MK D.PM PK B. Which statement correctly names two congruent segments? Example 1b

  14. Concept

  15. Concept

  16. Since QP = QR, QP  QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR. Find Missing Measures A. Find mR. Example 2

  17. Find Missing Measures B. Find PR. Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution. Example 2

  18. A. Find mT. A. 30° B. 45° C. 60° D. 65° Example 2a

  19. B. Find TS. A. 1.5 B. 3.5 C. 4 D. 7 Example 2b

  20. Find Missing Values ALGEBRA Find the value of each variable. Example 3

  21. Find the value of each variable. A.x = 20, y = 8 B.x = 20, y = 7 C.x = 30, y = 8 D.x = 30, y = 7 Example 3

  22. Given:HEXAGO is a regular polygon. ΔONG is equilateral, N is the midpoint of GE, and EX || OG. Prove:ΔENX is equilateral. ___ Apply Triangle Congruence Example 4

  23. Given: HEXAGO is a regular hexagon.NHE  HEN  NAG  AGN Prove: HN EN  AN  GN ___ ___ ___ ___ Proof: Statements Reasons 3. HE  EX  XA  AG  GO  OH 1. HEXAGO is a regular hexagon. 1. Given 2. NHEHENNAGAGN 2. Given 3. Definition of regular hexagon 4. ΔHNE  ΔANG 4. ASA Example 4

  24. Proof: Statements Reasons 5. HN  AN, EN NG 5. ___________ ? 6. HN  EN, AN  GN 6. Converse of Isosceles Triangle Theorem 7. HN  EN  AN  GN 7. Substitution A. Definition of isosceles triangle B. Midpoint Theorem C. CPCTC D. Transitive Property Example 4

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