Question

geometry
trapezoids practice
find the length of the diagonal indicated for each trapezoid.

1. ( rt = 20 )

find ( qs )

1. ( bd = 8 )

find ( ac )
solve for ( x ). each figure is a trapezoid.

1. ( km = 24 )

( jl = 11x - 9 )

1. ( tv = 10 )

( uw = 3x - 14 )
find the measurement of the angle indicated for each trapezoid.
5)
6)

Explanation:

1) For the trapezoid \( RQST \)

Step1: Use the property of isosceles trapezoid

In an isosceles trapezoid, the diagonals are equal. Since \( RQST \) is an isosceles trapezoid ( \( RS = QT \) as marked), and \( RT = 20 \), then \( QS=RT \).

2) For the trapezoid \( ABCD \)

Step1: Use the property of congruent triangles in trapezoid

In trapezoid \( ABCD \), \( \triangle BCD\cong\triangle ABC \) (by SSS - \( BC = BC \), \( CD = AB \) (marked), \( BD = AC \) (diagonals in a trapezoid with \( AD\parallel BC \) and non - parallel sides \( AB = CD \)). Given \( BD = 8 \), then \( AC=BD \).

3) For the trapezoid \( KJML \)

Step1: Set up the equation using diagonal property

In an isosceles trapezoid \( KJML \), the diagonals \( KM = JL \). Given \( KM = 24 \) and \( JL=11x - 9 \), we set up the equation \( 11x-9 = 24 \).

Step2: Solve the linear equation

Add \( 9 \) to both sides: \( 11x=24 + 9=33 \).
Divide both sides by \( 11 \): \( x=\frac{33}{11}=3 \).

4) For the trapezoid \( WTVU \)

Step1: Set up the equation using diagonal property

In an isosceles trapezoid \( WTVU \), the diagonals \( TV = UW \). Given \( TV = 10 \) and \( UW = 3x-14 \), we set up the equation \( 3x-14 = 10 \).

Step2: Solve the linear equation

Add \( 14 \) to both sides: \( 3x=10 + 14=24 \).
Divide both sides by \( 3 \): \( x=\frac{24}{3}=8 \).

5) For the trapezoid \( WXYV \)

Step1: Use the property of adjacent angles in a trapezoid

In an isosceles trapezoid \( WXYV \), adjacent angles along a non - parallel side are supplementary. If \( \angle X = 95^{\circ} \), then \( \angle V=180^{\circ}-\angle X \).

6) For the trapezoid \( VUTS \)

Step1: Use the property of adjacent angles in a trapezoid

In an isosceles trapezoid \( VUTS \), adjacent angles along a non - parallel side are supplementary. If \( \angle U = 110^{\circ} \), then \( \angle T=180^{\circ}-\angle U \).

Answer:

1. \( QS = 20 \)
2. \( AC = 8 \)
3. \( x = 3 \)
4. \( x = 8 \)
5. \( 85^{\circ} \)
6. \( 70^{\circ} \)