Question

congruent and similar figures given: abcd ≅ rstu ∠a≅ ∠c≅ ∠d≅ ab≅ da≅ st≅ given: △xyz≅ ∠z≅ ∠r≅ yz≅ ts≅ ***remember, if those corresponding parts are congruent, that means they have the exact same measurements! given: abcde ≅ jklmn jn = dc = kl = m∠d = m∠k =

Explanation:

Step1: Recall congruent - figure properties

In congruent figures, corresponding angles are equal and corresponding sides are equal.
For \(ABCD\cong RSTU\):

• \(\angle A\cong\angle R\), \(\angle C\cong\angle S\), \(\angle B\cong\angle T\), \(\angle D\cong\angle U\)
• \(\overline{AB}\cong\overline{RS}\), \(\overline{DA}\cong\overline{UR}\), \(\overline{ST}\cong\overline{BC}\)

Step2: Analyze second - set of congruent triangles

For \(\triangle XYZ\cong\triangle RST\):

• \(\angle Z\cong\angle T\), \(\angle R\cong\angle X\), \(\angle Y\cong\angle S\)
• \(\overline{YZ}\cong\overline{ST}\), \(\overline{TS}\cong\overline{ZY}\)

Step3: Analyze pentagons

For \(ABCDE\cong JKLMN\):

• \(JN = AE\), \(DC=ML\), \(KL = CB\)
• \(m\angle D=m\angle L\), \(m\angle K = m\angle B\)

Answer:

For \(ABCD\cong RSTU\): \(\angle A\cong\angle R\), \(\angle C\cong\angle S\), \(\angle B\cong\angle T\), \(\angle D\cong\angle U\), \(\overline{AB}\cong\overline{RS}\), \(\overline{DA}\cong\overline{UR}\), \(\overline{ST}\cong\overline{BC}\)
For \(\triangle XYZ\cong\triangle RST\): \(\angle Z\cong\angle T\), \(\angle R\cong\angle X\), \(\angle Y\cong\angle S\), \(\overline{YZ}\cong\overline{ST}\), \(\overline{TS}\cong\overline{ZY}\)
For \(ABCDE\cong JKLMN\): \(JN = AE\), \(DC = ML\), \(KL=CB\), \(m\angle D=m\angle L\), \(m\angle K=m\angle B\)