THEOREMS ON TRAPEZOIDS & MIDSEGMENT THEOREM | GRADE 9

Study the different theorems on trapezoid and the midsegment theorem A trapezoid is a convex quadrilateral with exactly one pair of parallel sides. The bases of a trapezoid are the two parallel sides. The legs of a trapezoid are the two non-parallel sides. An isosceles trapezoid is a trapezoid with congruent legs. The median of a trapezoid is the segment that joins the midpoints of the legs. Theorem 6: The median of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. •Theorem 7: The base angles of an isosceles trapezoid are congruent. •Theorem 8 : The opposite angles of an isosceles trapezoid are supplementary. •Theorem 9: The diagonals of an isosceles trapezoid are congruent. Sample Exercises: Given: Quadrilateral MATH is an isosceles trapezoid with bases MA and HT, LV is a median 1. Given: MA = 3y – 2; HT = 2y + 4; LV = 8.5 cm. Questions: • What is the value of y? • How did you solve for y? • What are MA and HT? 2. Given: angle HMA = 115 Questions: • What is m angle TAM? • What theorem justifies your answer? 3. Given: angle MHT = 3x + 10; angle MAT = 2x – 5 Questions: • What is the value of x? • How did you solve for x? • What are the measures of the two angles? • What theorem justifies your answer? 4. Given: AH = 4y – 3; MT = 2y +5 Questions: • What is the value of y? • How did you solve for y? • How long is each diagonal? • What theorem justifies your answer?