Answer:
Therefore,
ΔABD ~ ΔACB by Angle-Angle Similarity Postulate
AB is 8 unit.
Step-by-step explanation:
Given:
∠ABD ≅ ∠BCD
AD = 4
DC = 12 Therefore AC =AD + DC = 4 +12 =16
AC =16
To Find:
Similar Triangles
AB =?
Solution:
In ΔABD and ΔACB
∠ABD ≅ ∠ACB ……….{Given}
∠ A ≅ ∠ A .……..{Reflexive Property}
ΔABD ~ ΔACB ….{By Angle-Angle Similarity Postulate}
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{AB}{AC} =\dfrac{AD}{AB} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Substituting the values we get
[tex]\dfrac{AB}{16} =\dfrac{4}{AB}\\\\(AB)^{2}=64\\AB=\sqrt{64}=8\ unit[/tex]
Therefore,
ΔABD ~ ΔACB by Angle-Angle Similarity Postulate
AB is 8 unit.
