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Bell work: Identify all congruent triangles from the picture below

Learn about the properties of parallelograms, including congruent triangles and conditional statements, through theorem proofs and solving parallelograms. Homework exercises included.

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Bell work: Identify all congruent triangles from the picture below

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  1. Bell work: Identify all congruent triangles from the picture below

  2. 6.2: Properties of Parallelograms

  3. If Statements (AKA Conditional Statements) Recall… Theorem 6.2: The sum of the measures of the exterior angles of any polygon is 360

  4. If and Only If statements(AKA Biconditional statements) • A triangle has three equal sides if and only if it has three equal angles

  5. Notes • A parallelogram is a quadrilateral (4 sided shape) where the opposite sides are all parallel • In a quadrilateral, opposite angles are angles that share no side, and opposite sides are sides that share no vertex • For any polygon, consecutive angles are angles that are next to each other; ones that share a common side

  6. Theorem 6-3/6-8: A quadrilateral is a parallelogram…if and only ifits opposite sides are congruent • Theorem 6-4/6-9: A quadrilateral is a parallelogram…if and only ifits consecutive angles are supplementary • Theorem 6-5/6-10: A quadrilateral is a parallelogram…if and only ifits opposite angles are congruent • Theorem 6-6/6-11: A quadrilateral is a parallelogram…if and only ifits diagonals bisect each other

  7. What is the measure of angle P?

  8. If we adjust the lamp such that angle s=86, what would angle R be?

  9. Proofs of theorem 6-3 and 6-5

  10. Suppose I construct the diagonals of a parallelogram…

  11. In other words…if we have parallel lines where they are all crossed by the same line, and segments of that line are congruent, then any line that crosses the parallel ones will form segments of the same size

  12. 6.3: Proving a quadrilateral is a parallelogram

  13. Find a value for y that makes the shape a parallelogram

  14. For what values of x and y must the shape below be a parallelogram?

  15. Homework: • Section 6.2, page 364: 9, 13, 14, 15, 17, 21, 23, 27 • Honors: Add 28, 30, 38 • Section 6.3, page 372: 7-9, 13 • Honors: Add 16, 22, 23

  16. Find the value of each variable or side

  17. Section 6.3 13. Can you prove this is a parallelogram using the given information?

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