TechMathI - 5.6 - Trapezoids
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This document discusses properties and definitions related to trapezoids. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and defines an isosceles trapezoid as one where the non-parallel sides are congruent. It states that the diagonals of an isosceles trapezoid are congruent and that the median of any trapezoid is parallel to the bases and has a length that is half the sum of the base lengths. It includes examples of finding missing side lengths using the median property.
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- A polyomino made of 1 square would require 4 sticks
- A polyomino made of 2 squares would require 6 sticks
- A polyomino made of 3 squares would require 8 sticks
- A polyomino made of 4 squares would require 10 sticks (as in the example given)
- Continuing the pattern, a polyomino made of n squares would require 2n + 2 sticks
For the rectangle counting activity:
- There are 4 rectangles in the given diagram (
Module 3 geometry of shape and size
This module introduces quadrilaterals. It discusses identifying and naming quadrilaterals, the parts of a quadrilateral including sides, vertices, angles, and diagonals. It also defines different types of quadrilaterals including trapezoids, parallelograms, and trapeziums based on whether sides are parallel or perpendicular. Exercises are provided to help learn identifying quadrilaterals, their parts, and classifying them by type. The goal is to develop skills in recognizing quadrilaterals and understanding their applications.
CEM REVIEWER
Here are the solutions to the problems:
1. a) A lies in the interior of the circle because PA < PQ.
b) B lies in the exterior of the circle because PB > PQ.
c) The circles with radii PQ and PB are called concentric circles.
2. One tangent.
3. 12
4. 15
5. 16
MIDLINE THEOREM.pptx
The document discusses the midline theorem in geometry. The midline theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long. Several examples are provided to demonstrate using the theorem to solve for unknown side lengths of triangles.
Trapezoids
This document defines and describes properties of trapezoids and isosceles trapezoids. It defines a trapezoid as a quadrilateral with one set of parallel sides, called bases, and defines an isosceles trapezoid as having two congruent legs. The key properties outlined are that the leg angles are supplementary, base angles and diagonals of an isosceles trapezoid are congruent, and the midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. Several example problems are provided to demonstrate applying these properties.
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TechMathI - 5.6 - Trapezoids
- 2. Trapezoids *They have only one pair of opposite sides that are parallel leg leg base base
- 3. If the legs are congruent then the trapezoid is ISOSCELES
- 4. If a trapezoid is isosceles then each pair of base angles is congruent
- 5. Example 1 Find the other angles in this isosceles trapezoid. D A C B
- 6. If a trapezoid is isosceles then its diagonals are congruent
- 7. The MEDIAN connects the midpoints of the legs B A C D E F
- 8. Median Theorem for Trapezoids parallel to each base and its length is half the sum of the lengths of the bases
- 9. Which means…
- 10. Example 2 Find the length of the median MN in trapezoid ABCD if AB = 20 and CD = 16. D A C B M N
- 11. EXAMPLE 3 A D B C EF is the median of trapezoid ABCD. Find EF. E F 22 in. 10 in. EF = 16
- 12. EXAMPLE 4 M H A C BC is the median of trapezoid MATH. Find MA. B T 15 in. 22 in. MA = 8
- 13. EXAMPLE 5 T P R C BC is the median of trapezoid TRAP. Find TR. B A 19 in. 11 in. TR = 27