Given: RM = SN TM = TN Prove: RN = SM
1 answer:
I found the corresponding image as well as its statements and justifications that I have to match.
1. Given → RM = SN ; <span>TM = TN</span><span>
2. Reflexive </span>→ ∠T = ∠T<span>
3. Addition Property of Equality </span>→ RM + TM = SN + TN<span>
4. Betweeness </span>→ RT = ST<span>
5. Substitution </span>→ RM + TM = RT, SN + TN = ST<span>
6. SAS </span>→ Triangle RTN congruent to Triangle STM<span>
7. CPCTE </span>→ RM = SN
1. Given → RM = SN ; <span>TM = TN</span><span>
2. Reflexive </span>→ ∠T = ∠T<span>
3. Addition Property of Equality </span>→ RM + TM = SN + TN<span>
4. Betweeness </span>→ RT = ST<span>
5. Substitution </span>→ RM + TM = RT, SN + TN = ST<span>
6. SAS </span>→ Triangle RTN congruent to Triangle STM<span>
7. CPCTE </span>→ RM = SN
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Step-by-step explanation:
We know by the Triangle Angle-Sum Theorem that the angles of a triangle all add up to equal 180. So we find angle B:
180 - 82 - 55 = 43
So angle B = 43. Now we can use the Law of Sines to solve for side b:
Cross multiply to get
b sin(55) = 8 sin(43) and divide to solve for b:
so
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