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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Cumulative Assessment

Exercise 1 Page 538

The arcs are part of two identical circles. What is equivalent in two identical circles?

See solution.

Practice makes perfect

If CD is the perpendicular bisector of AB, two things have to be true.

CD has to bisect AB.
CD has to form a right angle with AB.

To prove this, we can think of the arcs as parts of two circles with A and B as midpoints and with identical radius. Therefore, if we draw AC, BC, AD, and BD, these segments will be congruent.

Examining the diagram, we see △ ABC and △ ABD. Since they both have a pair of congruent sides, they are isosceles triangles where C and D are the vertex angles of the triangles.

When drawing the height from the vertex angle of an isosceles triangle, it will bisect the base and intersect it at a right angle.

Therefore, we know that CD is the perpendicular bisector of AB.

Subchapter links

Exercises p.538-539