In ABCD, AB = AD and AC bisects A. Show that ABC ADC. And also write its remaining congruent parts.
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Answer: We know that AB = AD and a bisector of angle A is AC. Our aim is to prove that ABD is congruent with ACD.
AC is a bisector of A, then:
⇒ ∠DAC = ∠BAC
In ΔADC and ΔABC, we know that AD=AB and ∠DAC=∠BAC, hence:
⇒ AC = AC
By SAS, if two triangles have two equal sides or congruent sides, and an equal angle formed by these sides, then both triangles are congruent.
Hence, ΔABD ≅ ΔACD.
Step-by-step explanation:
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