Question

given: (overline{jk}congoverline{ml}), (angle jklcongangle mlk) prove: (\triangle jklcong\triangle mlk) statements reasons 1. (overline{jk}congoverline{ml}) 1. given 2. (angle jklcongangle mlk) 2. given 3. (overline{kl}congoverline{lk}) 3. reflexive 4. (\triangle jklcong\triangle mlk) 4. 21 given: (overline{ab}congoverline{cd}) (overline{bc}congoverline{da}) prove: (\triangle abccong\triangle cda) statements reasons 1. (overline{ab}congoverline{cd}) 1. given 2. (overline{bc}congoverline{da}) 2. given 3. (overline{ac}congoverline{ac}) 3. reflexive 4. (\triangle abccong\triangle cda) 4. 22

Explanation:

Question 21

To prove \(\triangle JKL \cong \triangle MLK\), we analyze the given statements:

1. \(JK \cong ML\) (Given)
2. \(\angle JKL \cong \angle MLK\) (Given)
3. \(KL \cong LK\) (Reflexive property, a side is congruent to itself)

These correspond to two sides and the included angle? No, wait, \(JK \cong ML\), \(\angle JKL \cong \angle MLK\), and \(KL\) is common. So the congruence criterion here is SAS (Side - Angle - Side). Because we have two sides (\(JK\) and \(KL\) for \(\triangle JKL\); \(ML\) and \(LK\) for \(\triangle MLK\)) and the included angle (\(\angle JKL\) and \(\angle MLK\)) congruent.

To prove \(\triangle ABC \cong \triangle CDA\), we analyze the given statements:

1. \(AB \cong CD\) (Given)
2. \(BC \cong DA\) (Given)
3. \(AC \cong AC\) (Reflexive property, a side is congruent to itself)

Here, we have three pairs of congruent sides: \(AB \cong CD\), \(BC \cong DA\), and \(AC \cong AC\). So the congruence criterion is SSS (Side - Side - Side).

Answer:

The reason is SAS (Side - Angle - Side) congruence criterion.

Question 22