Question

1. given that ( \triangle wnpcong\triangle zxy ), list all of the pairs of congruent sides and angles. (6 pts)

sides:________________________
________________________
________________________
angles:________________________
________________________
________________________
given that ( \triangle defcong\triangle kjl ), answer the following questions. (5 pts each)

1. ( kj=)
2. ( fd=)
3. ( mangle kjl=)
4. ( mangle edf=)
5. ( mangle jlk=)

Explanation:

Step1: Identify congruent sides and angles for \(\triangle WNP\cong\triangle ZXY\)

When two triangles are congruent, their corresponding parts (sides and angles) are congruent.
For \(\triangle WNP\) and \(\triangle ZXY\):

• Corresponding sides: \(WN = ZX\), \(NP=XY\), \(WP = ZY\)
• Corresponding angles: \(\angle W=\angle Z\), \(\angle N=\angle X\), \(\angle P=\angle Y\)

Step2: Solve for \(KG\) in \(\triangle DEF\cong\triangle KJL\)

Since \(\triangle DEF\cong\triangle KJL\), corresponding sides are equal.
\(KG = ED = 11\mathrm{cm}\)

Step3: Solve for \(FD\) in \(\triangle DEF\cong\triangle KJL\)

Corresponding sides: \(FD = JL\)
From the figure, \(JL = 16\mathrm{cm}\), so \(FD = 16\mathrm{cm}\)

Step4: Solve for \(m\angle KJL\) in \(\triangle DEF\cong\triangle KJL\)

Corresponding angles: \(\angle KJL=\angle DEF\)
From the figure, \(m\angle DEF = 82^{\circ}\), so \(m\angle KJL = 82^{\circ}\)

Step5: Solve for \(m\angle EDF\) in \(\triangle DEF\cong\triangle KJL\)

Corresponding angles: \(\angle EDF=\angle KJL\)
In \(\triangle KJL\), using the angle - sum property of a triangle (\(\angle K+\angle J+\angle L = 180^{\circ}\)), \(\angle K = 55^{\circ}\), \(\angle J = 82^{\circ}\)
\(\angle L=180-(55 + 82)=43^{\circ}\)
So \(m\angle EDF = 43^{\circ}\)

Step6: Solve for \(m\angle JLK\) in \(\triangle DEF\cong\triangle KJL\)

Corresponding angles: \(\angle JLK=\angle DFE\)
Since \(\angle DFE=\angle JLK\) and from the angle - sum property of \(\triangle DEF\) (\(\angle D+\angle E+\angle F=180^{\circ}\)), \(\angle E = 82^{\circ}\), \(\angle D = 43^{\circ}\)
\(\angle F=180-(82 + 43)=55^{\circ}\)
So \(m\angle JLK = 55^{\circ}\)

Answer:

1.

• Sides: \(WN = ZX\), \(NP = XY\), \(WP = ZY\)
• Angles: \(\angle W=\angle Z\), \(\angle N=\angle X\), \(\angle P=\angle Y\)

1. \(11\mathrm{cm}\)
2. \(16\mathrm{cm}\)
3. \(82^{\circ}\)
4. \(43^{\circ}\)
5. \(55^{\circ}\)