Question

problem 23
given: rhombus tcbv,
(overline {cu}perpoverline {bv},overline {cs}perpoverline {tv})
prove: (overline {cu}congoverline {cs})

1. rhombus tcbv,

(overline {cu}perpoverline {bv},overline {cs}perpoverline {tv})

1. (angle cst) and (angle cub) are

right angles.

1. (angle cstcongangle cub)

Explanation:

Step1: Definition of perpendicular lines

If two lines are perpendicular, then the angle between them is \(90^{\circ}\). Since \(\overline{CU}\perp\overline{BV}\) and \(\overline{CS}\perp\overline{TV}\), by the definition of perpendicular lines, \(\angle CST = 90^{\circ}\) and \(\angle CUB=90^{\circ}\).

Step2: Definition of congruent angles

Angles that have the same measure are congruent. Since \(\angle CST = 90^{\circ}\) and \(\angle CUB = 90^{\circ}\), then \(\angle CST\cong\angle CUB\) (because \(m\angle CST=m\angle CUB = 90^{\circ}\)).

Answer:

1. Definition of perpendicular lines; 3. All right angles are congruent.