Bell work: Identify all congruent triangles from the picture below

6.2: Properties of Parallelograms

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

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

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

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

What is the measure of angle P?

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

Proofs of theorem 6-3 and 6-5

Suppose I construct the diagonals of a parallelogram…

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

6.3: Proving a quadrilateral is a parallelogram

Find a value for y that makes the shape a parallelogram

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

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

Find the value of each variable or side

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