Draw a segment and let its length be 1.a. Construct a segment of length \ 5,_ ^ 1 \5 1 +

Given: AJKM Explain how to construct a triangle that is congruent to AJKM.

Draw any AB. a. Construct XY so that XY = AB. b. Using X and Y as centers, and a radius equal to AB, draw arcs that intersect. Label the point of intersection Z. c. Draw XZ and YZ. d. What kind of triangle is AATZ?

Explain how you could construct a 30 angle.

Exercise 3 suggests that you could construct other angles with certain measures. Name some.

Suppose you are given the three lengths shown and are r asked to construct a triangle whose sides have lengths r, s, and t. Can you do so? State the theorem from # Chapter 6 that applies.

Z 1 and Z2 are given. You see two attempts at constructing an angle whose measure is equal to wZl + mZ2. Are both constructions satisfactory?

A square whose sides each have length AC

A square whose perimeter equals AC

A right triangle with hypotenuse and one leg equal to AC and BC, respectively

A triangle whose sides are in the ratio 1 :2:\/3

Where does the center of the circle lie with respect to line / and point X?

Where does the center of the circle lie with respect to AY?

Explain how to carry out the construction of the circle.

a. Draw an acute triangle. Construct the perpendicular bisector of each side. b. Do the perpendicular bisectors intersect in one point? c. Repeat parts (a) and (b) using an obtuse triangle.

a. Draw an acute triangle. Construct the three altitudes. b. Do the lines that contain the altitudes intersect in one point? c. Repeat parts (a) and (b) using an obtuse triangle.

a. Draw a very large acute triangle. Construct the three medians. b. Do the lines that contain the medians intersect in one point? c. Repeat parts (a) and (b) using an obtuse triangle.

A parallelogram with an n angle and sides of lengths a and b

A rectangle with sides of lengths a and b

A square with perimeter 2a

A rhombus with diagonals of lengths a and b

A square with diagonals of length

A segment of length \Ja 2 + b 2

A square with diagonals of length b\J2

A right triangle with hypotenuse of length a and one leg of length b

Drawji segment and let its length be s. Construct a segment whose length is sv3.

Draw a diagram roughly like the one shown. Without laying your straightedge across any part of the lake, construct more of RS.

Draw three noncollinear points R, S, and T. Construct a triangle whose sides have R, S, and T as midpoints. (Hint: How is RT related to the side of the triangle that has 5 as its midpoint?)

Draw a segment and let its length be 1. a. Construct a segment of length \ 5 ,_ ^ 1 \5 1 + \ 5 b. Construct a segment of lensth I . or . *" 2 2 2 c. Construct a golden rectangle (as discussed on page 253) whose sides 1 + \5 are in the ratio 1 : .