Question

find each measure.

1. rs
2. xz

list the angles and sides of each triangle in order from smallest to largest.
3.
4.

Explanation:

Step1: Solve for RS (Triangle 1)

Line QT is the perpendicular bisector of RS, so $RQ = QS = 4.5$. $RS = RQ + QS$
$RS = 4.5 + 4.5$

Step2: Solve for y (Triangle 2)

Line XW is the perpendicular bisector of ZY, so $XZ = XY$. Set sides equal:
$5y - 6 = 18 + 2y$
$5y - 2y = 18 + 6$
$3y = 24$
$y = 8$

Step3: Calculate XZ (Triangle 2)

Substitute $y=8$ into $XZ = 5y - 6$:
$XZ = 5(8) - 6$

Step4: Order triangle 3 sides/angles

Side order: $RT=5 < TS=6 < SR=7$. Angle order (opposite sides): $\angle S < \angle R < \angle T$

Step5: Find $\angle C$ (Triangle 4)

Sum of angles in triangle is $180^\circ$:
$\angle C = 180^\circ - 46^\circ - 74^\circ = 60^\circ$

Step6: Order triangle 4 angles/sides

Angle order: $\angle A=46^\circ < \angle C=60^\circ < \angle B=74^\circ$. Side order (opposite angles): $BC < AC < AB$

Answer:

1. $RS = 9$
2. $XZ = 34$
3. Sides (smallest to largest): $RT, TS, SR$; Angles (smallest to largest): $\angle S, \angle R, \angle T$
4. Angles (smallest to largest): $\angle A, \angle C, \angle B$; Sides (smallest to largest): $BC, AC, AB$