Question

Which of the following shows that △ABD≅△CBD, when y=5?

Answer 1

Answer:

The correct option is;

∠ADB ≅ ∠CDB, $\overline {BD}$ ≅ $\overline {BD}$ and $\overline {AD}$ ≅ $\overline {CD}$. So ΔABD ≅ ΔCDB by SAS

Step-by-step explanation:

The given parameters are;

The polygon given = Quadrilateral

The diagonal of the quadrilateral = BD

The length of the side AD = (2×y + 5) units

The length of the side CD = (y + 10) units

The given measure of ∠ABD = (2 × y + 25)°

The given measure of ∠CBD = 35°

When y = 5, we have by substituting the value of y into the equations representing the dimensions of the quadrilateral ABCD;

The length of the side AD = 2 × y + 5 = 2×5 + 5 = 15 units

∴ The length of the side AD = 15 units

The length of the side CD = (y + 10) units = (5 + 10) units = 15 units

∴ The length of the side CD = 15 units

The measure of ∠ABD = (2 × y + 25)° = (2 × 5 + 25)° = 35°

The measure of ∠ABD = 35°

Therefore;

∠ADB ≅ ∠CDB by substitution

$\overline {BD}$ ≅ $\overline {BD}$ by reflexive property

$\overline {AD}$ ≅ $\overline {CD}$ by substitution

∴ ΔABD ≅ ΔCBD by Side-Angle-Side rule of congruency