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4/6 Geometry Bell Ringer Find mM and solve for x: Homework: FINISH TODAY’S INDEPENDENT PRACTICE News and Notes • Perfection: 4th • REPORT CARDS TOMORROW! EXTRA CREDIT!! • ACT Workshop today after school in 218. Perfection Competition Daily Results 1 1 1 0.8 0.6 0.4 0.2 0 1st 2nd 4th 7th 8th Yesterday: • We investigated missing angles of quadrilaterals. Today: • Discover properties of two special types of quadrilaterals: Kites and Trapezoids. • GET OUT YOUR VOCAB TREE • Imagine Quadrilateral is the grandparent • Kite, Parallelogram and Trapezoid are parents 4 SI DES • What’s the link between grandparents and parents? • Now let’s discover some specific properties for kites and trapezoids. We will start with a kite. Kreate-A-Kite • Step 1: On patty paper, draw two connected segments of different lengths. • Step 2: Fold through endpoints and trace the two line segments. • Step 3: Open up the paper, answer questions 1! Question 1 • What appears to be true regarding the angles of a kite? • KITE ANGLE CONJECTURE: Kites have one pair of opposite angles congruent Question 2: • What appears to be true about the sides of the kite? • KITE SIDE CONJECTURE: Kites have two pairs of congruent sides Back to the Patty Paper • Step 4: Draw the diagonals of the kite (connect opposite vertices). • Step 5: Answer question #3. Question #3 • How are the diagonals related? • KITE DIAGONALS CONJECTURE: The diagonals of a kite are perpendicular and one is bisected by the other What’s so special about a kite? 2 pairs of congruent sides 1 pair of congruent angles Diagonals are perpendicular Small diagonal is bisected Now on to trapezoids • What is a trapezoid? • A quadrilateral with ONE pair of parallel sides. • So does this work? 1 pair of parallel sides. Consecutive angles are supplem. What makes it isosceles or right? • What was an isosceles triangle? A triangle with 2 congruent sides and angles. • So what is an isosceles trapezoid? A trapezoid with 2 congruent sides (not the parallel ones) and 2 pairs of congruent angles. DRAW ONE!!! 2 congruent sides 2 pairs congruent angles Diagonals congruent What is a right trapezoid? 1 right angle PRACTICE UNTIL EXIT TICKET!!! EXIT TICKET • 1) Given that the following trapezoid is isosceles, solve for x, y, and z. x° 7 ft 70° 110° z y° • 2) What is the relationship between the opposite angles?