91Ó°ÊÓ

Given \(\triangle \mathrm{ABC}\), construct a line parallel to \(\overrightarrow{\mathrm{AB}}\) and passing through C.

Sketch all possible intersections for each compound locus. Then describe the compound locus. a The locus of points equidistant from two given points and lying on a given circle b The locus of points that are a given distance from a point A and another given distance from a point B c The locus of points on both the graph of \(y=5\) and the graph of \(x^{2}+y^{2}=r^{2},\) where \(r>0\) d The locus of points equidistant from two parallel lines and lying on a third line e The locus of points equidistant from two intersecting lines and a fixed distance from their point of intersection f The locus of points equidistant from the sides of an angle and equidistant from two parallel lines

Construct the locus of points equidistant from two fixed points A and B.

Draw two segments, \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}},\) with \(\mathrm{AB}>\mathrm{CD}\). a Construct a segment whose length is the sum of AB and CD. b Construct a segment whose length is the difference of AB and CD. c Locate the midpoint of \(\overline{\mathrm{AB}}\) by construction. d Construct an equilateral triangle whose sides are congruent to \(\overline{\mathrm{CD}}\). e Construct an isosceles triangle, making its base congruent to \(\overline{\mathrm{CD}}\) and each leg congruent to \(\overline{\mathrm{AB}}\). f Construct a square whose sides are congruent to \(\overline{\mathrm{AB}}\). g Construct a circle whose diameter is congruent to CD.

Construct an isosceles triangle, given a The vertex angle and a leg b The base and the altitude to the base

Given \(\overline{\mathrm{AB}}\), with point \(\mathrm{C}\) between \(\mathrm{A}\) and \(\mathrm{B}\), construct a segment whose length is the mean proportional between \(\mathrm{AC}\) and \(\mathrm{BC}\).

Given scalene \(\triangle\) DEF, explain how to find the locus of points equidistant from \(\overline{\mathrm{DE}}, \mathrm{EF},\) and \(\overline{\mathrm{DF}}\).

How many points are equidistant from two given parallel lines and equidistant from two fixed points on one of those lines?

Construct an isosceles right triangle, given a A leg b The hypotenuse

Draw an acute angle \(A B C\) and an obtuse angle \(W X Y\). a Construct \(\angle \mathrm{FGH}\) congruent to \(\angle \mathrm{WXY}\). b Construct the complement of \(\angle \mathrm{ABC}\). c Construct the supplement of \(\angle \mathrm{WXY}\). d Construct an angle whose measure is the difference of \(\angle \mathrm{WXY}\) and \(\angle \mathrm{ABC}\). e Construct an angle whose measure is double that of \(\angle \mathrm{ABC}\).