SOLUTION: How do I prove two triangles congruent in a quadrilateral? I already have two angles congruent, because it is in the given info. Also they gave me a pair of congruent lines, what's

Question 622241: How do I prove two triangles congruent in a quadrilateral? I already have two angles congruent, because it is in the given info. Also they gave me a pair of congruent lines, what's next? Is it another angle? Please help.
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
I can't see your figure, so I'll guess it's something like
this. You have a kite ABCD with a diagonal AC:

Given: AB ≅ AD
∠ABC ≅ ∠ADC
Prove: ᐃABC ≅ ᐃADC
I'll just give you an outline. You'll have to write the
2-column proof.
Draw BD:

Then ᐃABD is isosceles because its legs AB and AD are given congruent. Therefore
base angles ∠ABD ≅ ∠ADB. Since we are given
∠ABC ≅ ∠ADC, then m∠ABD = m∠ADC. Since ∠ABD ≅ ∠ADB, m∠ABD = m∠ADB.
Subtracting equals from equals, we get that m∠CBD = m∠CDB and ∠CBD ≅ ∠CDB.
Therefore ᐃBCD is isosceles because its base angles are congruent.
BC ≅ DC because they are legs of isosceles ᐃBCD. Now we have
AB ≅ AD, ∠ABC ≅ ∠ADC, BC ≅ DC. Then ᐃABC ≅ ᐃADC by SAS.
Edwin
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