Question

complete the following proofs by matching the statements to the reasons.

given: \\(\angle 1 \cong \angle 2\\); \\(\angle 3 \cong \angle 4\\)

prove: \\(\triangle jkl\\) is an isosceles triangle

• \\(\angle 1 \cong \angle 2\\); \\(\angle 3 \cong \angle 4\\)
• \\(km \cong km\\)
• \\(\triangle jkm \cong \triangle lkm\\)
• \\(jk \cong kl\\)
• \\(\triangle jkl\\) is an isosceles triangle

Explanation:

Identify the given statements and reasons

Using the Reflexive Property of Congruence, ASA Congruence Postulate, and CPCTC knowledge points

• Statement 1: \(\angle 1 \cong \angle 2\); \(\angle 3 \cong \angle 4\) is Given.
• Statement 2: \(KM \cong KM\) is Reflexive.
• Statement 3: \(\triangle JKM \cong \triangle LKM\) is ASA.
• Statement 4: \(JK \cong KL\) is CPCTC.
• Statement 5: \(\triangle JKL\) is an isosceles triangle is Definition of Isosceles Triangle.

Answer:

Complete the following proofs by matching the statements to the reasons.

Given: \(\angle 1 \cong \angle 2\); \(\angle 3 \cong \angle 4\)

Prove: \(\triangle JKL\) is an isosceles triangle

• \(\angle 1 \cong \angle 2\); \(\angle 3 \cong \angle 4\) <blank>Given</blank>
• \(KM \cong KM\) <blank>Reflexive</blank>
• \(\triangle JKM \cong \triangle LKM\) <blank>ASA</blank>
• \(JK \cong KL\) <blank>CPCTC</blank>
• \(\triangle JKL\) is an isosceles triangle <blank>Definition of Isosceles Triangle</blank>