Trapezoids and Kites

Trapezoids and Kites A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are of trapezoid are called bases. The nonparallel sides are called legs. The two angles that share a base of a trapezoid are called base angles. A trapezoid has two pairs of base angles.

Trapezoids and Kites An isosceles trapezoid is a trapezoid with legs that are congruent. ABCD below is an isosceles trapezoid. The angles of an isosceles trapezoid have some unique properties.

Trapezoids and Kites

Trapezoids and Kites

Trapezoids and Kites Problem 1: CDEF is an isosceles trapezoid and m<C = 65. What are m<D, m<E, and m<F?

Trapezoids and Kites Problem 1b: PQRS is an isosceles trapezoid and m<R = 106. What are m<P, m<Q, and m<S?

Trapezoids and Kites Problem 2: The second ring of the paper fan consists of 20 congruent isosceles trapezoids that appear to form circles. What are the measures of the base angles of these trapezoids?

Find the measures of the numbered angles in each isosceles trapezoid. Trapezoids and Kites Problem 3: Find the measures of the numbered angles in each isosceles trapezoid.

Find the measures of the numbered angles in each isosceles trapezoid. Trapezoids and Kites Problem 3b: Find the measures of the numbered angles in each isosceles trapezoid.

Find the measures of the numbered angles in each isosceles trapezoid. Trapezoids and Kites Problem 3c: Find the measures of the numbered angles in each isosceles trapezoid.

Trapezoids also have midsegments. Trapezoids and Kites In lesson 5.1 you learned about the midsegments of triangles…What are they???? Trapezoids also have midsegments. The midsegment of a trapezoid is the segment that joins the midpoints of its legs. The midsegment has two unique properties.

Trapezoids and Kites

Problem 4: Segment QR is the midsegment of trapezoid LMNP. What is x? Trapezoids and Kites Problem 4: Segment QR is the midsegment of trapezoid LMNP. What is x?

Problem 4b: Find EF is the trapezoid. Trapezoids and Kites Problem 4b: Find EF is the trapezoid.

Problem 4c: Find EF is the trapezoid. Trapezoids and Kites Problem 4c: Find EF is the trapezoid.

Find the lengths of the segments with variable expressions. Trapezoids and Kites Problem 4e: Find the lengths of the segments with variable expressions.

Trapezoids and Kites A kite is a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.

Trapezoids and Kites

Quadrilateral DEFG is a kite. What are m<1, m<2, m<3? Trapezoids and Kites Problem 5: Quadrilateral DEFG is a kite. What are m<1, m<2, m<3?

Section 6.6 – Trapezoids and Kites Problem 5b: Find the measures of the numbered angles in each kite.

Problem 5c: Find the measures of the numbered angles in each kite. Trapezoids and Kites Problem 5c: Find the measures of the numbered angles in each kite.

Problem 5d: Find the measures of the numbered angles in each kite. Trapezoids and Kites Problem 5d: Find the measures of the numbered angles in each kite.

Problem 5e: Find the value(s) of the variable(s) in each kite. Trapezoids and Kites Problem 5e: Find the value(s) of the variable(s) in each kite.

Problem 5f: Find the value(s) of the variable(s) in each kite. Trapezoids and Kites Problem 5f: Find the value(s) of the variable(s) in each kite.

Section 6.6 – Trapezoids and Kites

Trapezoids and Kites Problem 6: Determine whether each statement is true or false. Be able to justify your answer. All squares are rectangles A trapezoid is a parallelogram A rhombus can be a kite Some parallelograms are squares Every quadrilateral is a parallelogram All rhombuses are squares.

Trapezoids and Kites Problem 7: Name each type of quadrilateral that can meet the given condition. Exactly one pair of congruent sides Two pairs of parallel sides Four right angles Adjacent sides that are congruent Perpendicular diagonals Congruent diagonals

Trapezoids and Kites Problem 8: Can two angles of a kite be as follows? Explain! Opposite and acute Consecutive and obtuse Opposite and supplementary Consecutive and supplementary Opposite and complementary Consecutive and complementary

Trapezoids and Kites Problem 8: Can two angles of a kite be as follows? Explain! Opposite and acute Consecutive and obtuse Opposite and supplementary Consecutive and supplementary Opposite and complementary Consecutive and complementary

Trapezoids and Kites