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Warm up (TI)

H. I. K. J. Warm up (TI). Name all pairs of consecutive angles. Name all pairs of opposite vertices. Name all pairs of consecutive sides. Name all diagonals. Find the missing measure if 3 of the 4 angles below are 90, 75, and 25. Parallelograms. Unit 3 Concept 5.

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Warm up (TI)

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  1. H I K J Warm up (TI) • Name all pairs of consecutive angles. • Name all pairs of opposite vertices. • Name all pairs of consecutive sides. • Name all diagonals. • Find the missing measure if 3 of the 4 angles below are 90, 75, and 25.

  2. Parallelograms Unit 3 Concept 5

  3. Special Quadrilaterals! • A parallelogram is a special quad with both pairs of opposite sides parallel!

  4. NAME: FAKE Parallelograms… • Symbol F A E K

  5. Special properties!!! • Opposite angles are congruent. • Opposite sides are congruent. • Consecutive angles are supplementary. • Diagonals bisect each other.

  6. Examples • In KLMN, KL = 23, KN = 15, and m<K = 105. • Find LM and MN. • Find m<M. • Find m<L. 23 K L 105 15 N M

  7. Examples • In PQRS, if PR = 32, find PL. P Q L R S

  8. Guided Practice • Find the value of each variable in the parallelogram: 1. 2. 3. 4. 16 2a + 1 10 7 2b - 3 2x y + 2 21 52 º 4(p º +3) 4mº 135 º

  9. More Practice… • Find the indicated measure in PQRS. • PR • ST • mSRQ • m PQR Q P 3m 2n T 12 - n 15 2xº S R 5(x+1)º

  10. Finding the Intersection of Diagonals (Teacher Demo using Midpoint) The vertices of ABCD are A (-1,6), B (5, 6), C (3, -2), and D (-3, -2). The diagonals intersect at point P. What are the coordinates of P? A B P D C

  11. Practice… • The vertices of ABCD are A (-4, 2), B (3, 2), C (1, -1) and D (-6, -1). The diagonals intersect at point P. What are P’s coordinates?

  12. Theorem • A diagonal of a parallelogram separates it into two congruent triangles. R B T A

  13. Complete Properties of Parallelograms Worksheet • Turn in for a daily grade!

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