Write a paragraph proof for the following given- AD bisects CB and AD is perpendicular to CB. Prove- triangle ACD = triangle ABD
To prove that triangle ACD is congruent to triangle ABD, we can use the information given that AD bisects CB and that AD is perpendicular to CB.
First, we know that AD bisects CB. This means that it divides CB into two equal parts. Let's call the point where AD intersects CB as E. So, we have CE = EB.
Next, we are given that AD is perpendicular to CB. This means that angle ADC is a right angle.
Now, let's consider triangle ACD and triangle ABD. We can see that they share a common side, AD.
By the reflexive property of equality, we know that segment AD is equal to itself.
We also know that angle ADC is congruent to angle ADB since they are both right angles.
Finally, we have CE = EB from the fact that AD bisects CB.
Using the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle ACD is congruent to triangle ABD.