Question

I’m really bad at proofs like really bad can someone help with 20 and 21

Answer 1

Step-by-step explanation:

20.

In each proof, start by looking at what you're trying to prove.  We want to prove that two triangles are congruent.  To do that we use one of the following: SSS, SAS, ASA, or AAS.

To decide which one to use, look at the information given.  We're given two pairs of congruent sides, so we can narrow the strategy down to either SSS or SAS.  We aren't told anything about the third pair of sides, but we can see that ∠JNK and ∠MNL are vertical angles.  We'll use this to show the triangles are congruent by SAS.

1. JN ≅ MN, Given

2. ∠JNK ≅ ∠MNL, Vertical angles

3. NK ≅ NL, Given

4. ΔJNK ≅ ΔMNL, SAS

21.

Repeat the same steps as 20.  Again, we're trying to prove two triangles are congruent, so we have 4 strategies to choose from.  Just like before, we're given two pairs of congruent sides, so we'll use either SSS or SAS.  And again, we aren't told anything about the third pair of sides, but we can see that both triangles are right triangles.  So we'll use SAS again.

1. MN ≅ PQ, Given

2. ∠LMN ≅ ∠NQP, Right angles are congruent

3. LM ≅ NQ, Given

4. ΔNML ≅ ΔPQN, SAS