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Triangle Angle Measures and Classification Explanation

Learn to find and classify triangle angles, understand congruent figures, corresponding parts, the Third Angle Theorem, and properties of congruent triangles with examples and assignments.

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Triangle Angle Measures and Classification Explanation

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  1. Warm up (TI) Find the measure of each angle of the triangles given below. Then classify the triangle by its angles. • m<A = 2x + 5, m<B = 3x – 15, m<C = 4x + 10. • m<K = 10(x + 1), m<L = 9x – 3, m<M = 7x – 9.

  2. Congruence and Triangles Chapter 4 Section 2

  3. Congruent Figures • Two geometric figures are congruent if they have the same size and shape. • Same size implies same side lengths. • Same shape implies same angle measures.

  4. Corresponding parts.. • When two figures are congruent, their corresponding angles are congruent and their corresponding sides are congruent. ~ ∆ABC = ∆DEF D A F B C E

  5. Examples • Write a congruence statement for the triangles below. Identify all pairs of corresponding parts. Y H K Z X J

  6. Example ~ • In the diagram, ABCD = KJHL • Find the value of x. • Find the value of y. K A 9 cm B L 91° 4x - 3 5y - 12 86° 113° D C H J 6 cm

  7. Third Angle Theorem • If two angles of a triangle are congruent to two angles of another triangle, then the third angles are also congruent.

  8. Example • Find the value of x. 4x + 15 87° 22°

  9. Are these triangles congruent? If so…write a congruence statement. • Ask yourself…Are all corresponding parts congruent? • Is there anything that I can add to the diagram…(you must be able to justify anything that you add!) 21 4 21 4

  10. Properties of Congruent Triangles • Reflexive property: Every triangle is congruent to itself. • Symmetric property: If ∆ABC = ∆DEF then ∆DEF = ∆ABC. • Transitive property: If ∆ABC = ∆DEF and ∆DEF = ∆JKL, then ∆ABC = ∆JKL. ~ ~ ~ ~ ~

  11. Example • Given MN = QP, MN PQ, O is the midpoint of MQ and PN. • How do we know that ∆MNO = ∆QPO? ~ ~ M N O Q P

  12. Are there congruent triangles in this picture? If so write a congruence statement! A D B C

  13. Assignment Complete assignment 2 and notecards!

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