answer dis asap and Please show d working
Answers
Answer:
CD BISECTS ABC.
CA AND CB ARE EQUAL, SO IT'S AN ISOSCELES TRIANGLE
THEREFORE: CAD = CBD
Step-by-step explanation:
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Given:
- AC = BC (△ ACB is isosceles)
- CD is the bisector of ∠ACB
To prove:
∠CAD = ∠CBD
Solution:
As it is given that CD cuts ∠ACB into two equal halves (bisection), two triangles are formed within △ACB:
- △ACD
- △BCD
If these two triangles are congruent, ∠CAD will be equal to ∠CBD. Let us find the measures of the triangles.
In △ACD and △BCD,
- AC = BC (given)
- CD = CD (common side)
- ∠ACD = ∠BCD (CD is the bisector of ∠ACB)
We see that two of the sides and the included angle in △ACD is equal to the corresponding sides and angle of the other. This is the Side-Angle-Side criterion. Therefore,
△ACD ≅ △BCD
Which means that ∠CAD and ∠CBD are equal.
Hence, proved!
Congruence Criterions
These are some criterions to prove two triangles congruent:
- Side-Side-Side
If the measures of the sides of one triangle are equal to the other's, the triangles are congruent by SSS criterion.
- Side-Angle-Side
If two sides and the angle between them in a triangle are equal to the other triangle's corresponding sides and angle, the triangles are congruent by SAS criterion.
- Angle-Side-Angle
If two angles and the side between them in one triangle is equal to the corresponding ones of the other's, the triangles are congruent by ASA criterion.
- Right Angle-Hypotenuse-Side (only for right angled triangles)
If the hypotenuse and one leg of a right angled triangle is equal to the hypotenuse and the corresponding leg of the other, the triangles are congruent by RHS criterion.
