In Figure, $A B = A D$ and $∠ B A C = ∠ D A C$ .

(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.

(ii) Complete each of the following, so as to make it true:

(a) $∠ A B C =$

(b) $∠ A C D =$

(c) Line segment AC bisects ….. And ……..

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Solution

i) AB = AD (given)

$∠ B A C = ∠ D A C (g i v e n)$

AC = CA (common)

Therefore by SAS condition of congruency, ΔABC ≅ ΔADC

ii) $∠ A B C = ∠ A D C$ (corresponding parts of congruent triangles)

$∠ A C D = ∠ A C B$ (corresponding parts of congruent triangles)

Line segment AC bisects $∠ A a n d ∠ C .$

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In Figure, AB=AD and ∠BAC = ∠DAC. (i) State in symbolic form the congruence of two triangles ABC and ADC that is true. (ii) Complete each of the following, so as to make it true: (a) ∠ABC= (b) ∠ACD= (c) Line segment AC bisects ….. And ……..

i) AB = AD (given) ∠BAC=∠DAC (given) AC = CA (common) Therefore by SAS condition of congruency, ΔABC ≅ ΔADC ii) ∠ABC=∠ADC (corresponding parts of congruent triangles) ∠ACD=∠ACB (corresponding parts of congruent triangles) Line segment AC bisects ∠A and ∠C.

In Figure, $A B = A D$ and $∠ B A C = ∠ D A C$ .

(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.

(ii) Complete each of the following, so as to make it true:

(a) $∠ A B C =$

(b) $∠ A C D =$

(c) Line segment AC bisects ….. And ……..