MATH SOLVE

3 months ago

Q:
# plz plz help me friendsIn addition to the facts in the diagram, which other statements are necessary to prove that ∆ABC is congruent to ∆EFG by the ASA criterion?i. m∠B = m∠Fii. BC = FGiii. m∠A = m∠Eiv. FG = 3v. m∠B = m∠EA. i onlyB. iii or v onlyC. i and iii onlyD. i or iv only

Accepted Solution

A:

Answer:The answer is i and iii only ⇒ answer CStep-by-step explanation:* Lets revise the cases of congruence- SSS ⇒ 3 sides in the 1st Δ ≡ 3 sides in the 2nd Δ - SAS ⇒ 2 sides and including angle in the 1st Δ ≡ 2 sides and including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ
≡ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the first triangle ≡ 2 angles
and one side in the 2ndΔ
- HL ⇒ hypotenuse leg of the first right angle triangle ≡ hypotenuse
leg of the 2nd right angle Δ
* Lets solve the problem- From the figure in Δ ABC and Δ EFG∵ AB = 2 units∵ ∠A and ∠B are the end vertex of AB∵ EF = 2 units∵∠E and ∠F are the end vertex of EF∴ Δ ABC is congruent to Δ EFG if:# m∠B = m∠F# m∠A = m∠E∴ The necessary statements to prove that Δ ABC is congruent to Δ EFG by ASA are: i. m∠B = m∠F iii. m∠A = m∠E* The answer is i and iii only