Triangles δabc ≅ δbad so that c and d lie in the opposite semi-planes of segment ab. prove that segment cd bisects segment ad.

Congruent triangles are triangles with equal corresponding sides.

See below for the required proof

From the question, we have:

The above means that, the following sides are congruent

Similarly, the following angles are corresponding

By vertical angle theorem, we have the following corresponding angles:

Notice that points A and D are common in the above angles

So, we have:

Hence,

Line segment CD bisects line segment AD

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See explanation

Step-by-step explanation:

Triangles ΔABC and ΔBAD are congruent. So,

Consider triangles AEC and BED. In these triangles,

So, ΔAEC ≅ ΔBED. Thus,

AE ≅ EB.

This means that segment CD bisects segment AD.

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step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it