Unit 2, Lesson 8
The Perpendicular Bisector Theorem
Integrated Math 1
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Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment. Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.
Statement: If a triangle is isosceles, the base angles are congruent. Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.
Statement: If 2 angles form a straight angle, then they are supplementary. Converse: If 2 angles are supplementary, then they form a straight angle.
In isosceles triangle
Han and Priya were making a kite. Han cut out a piece of fabric so that there were two short sides of the same length on top and two long sides of the same length on the bottom. Priya cut two pieces of wood to go across the diagonals of the kite. They attached the wood like this:
Han asked Priya to measure the angle to make sure the pieces of wood were perpendicular. Priya said, “If we were careful about the lengths of the sides of the fabric, we don’t need to measure the angle. It has to be a right angle.”
Complete Priya’s explanation to Han.
Prove triangle
Triangle
Write a sequence of rigid motions to take figure
Two figures, C B A and M L K, each composed of two line segments that share an endpoint . A B slants upward and to the left and B C slants upward and to the right. Figure M L K is below and to the right of figure C B A. K L slants upward and to the left and L M slants upward and slightly to the left. B C and L M have one tick mark. A B and K L have two tick marks. Angles B and L marked equal.
Here is a quadrilateral inscribed in a circle.
Jada says that it is square because folding it along the horizontal dashed line and then the vertical dashed line gives 4 congruent sides. Do you agree with Jada?