4) Consider triangles ABC and A'B'C'. Extend side AB to a point D such that A*B*D. Extend side A'B' to a point D' such that A'*B’*D'. Let |AB| = |A’B’|, |BD| = |B'D'|, |AC|=|A'C'|, |BC|=|B'C'. Prove that |CD| = |C'D'|.

Which part hypothesis or conclusion of a theorem determines the a Drawing? b Given? c Prove?

Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle.

A quadrilateral RSTV is circumscribed about a circle so that its tangent sides are at the endpoints of two intersecting diameters. aWhat types of quadrilateral is RSTV? bIf the diameters are also perpendicular, what type of quadrilateral is RSTV?

The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340 miles on the north, 515 miles on the east, 435 miles on the south and 225 miles on the west. If A and B are points located midway across the north and south boundaries, what is the approximate distance from A to B?

Let all of the lines named be coplanar. Make a drawing to reach a conclusion. a If rs and st, then _. b If ab and bc, then _.

Two sets of rails railroad tracks are equally spaced intersect but not at right angles. Being as specific as possible, indicate what type of quadrilateral WXYZ is formed.

Use Figure 5.19 to prove Theorem 5.4.2. Theorem 5.4.2 The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

a. Suppose that you wish to prove that RSTSRV. Using the reason Identity, name one pair of corresponding parts that are congruent. b. Suppose you wish to prove that RWTSWV. Considering the figure, name one pair of corresponding angles of these triangles that must be congruent.

a Does the similarity relationship have a reflexive property for triangles and polygons in general? b Is there a symmetric property for the similarity of triangles and polygons? c Is there a transitive property for the similarity of triangles and polygons?