i have to proof that segment ad is congruent to segment ce. my givens are that segment ab is congruent to cb, that fd bisects ab and that fe bisects cb. the shape is a triangle

Question

i have to proof that segment ad is congruent to segment ce. my givens are that segment ab is congruent to cb, that fd bisects ab and that fe bisects cb. the shape is a triangle

Answer 1

since fd bisects ab, ad = db

since fe bisects bc. be = ce

since ab = bc,
ad+db = be+ce
ad+ad = ce+ce
ad = ce

Answer 2

To prove that segment AD is congruent to segment CE in the given triangle, we can use the properties of triangle congruence and angle bisectors.

Here's a step-by-step proof:

Step 1: Given that segment AB is congruent to segment CB.
Step 2: Given that segment FD bisects segment AB.
Step 3: Given that segment FE bisects segment CB.
Step 4: Define point D as the intersection of segment FD and segment CE.
Step 5: Define point E as the intersection of segment FE and segment AD.
Step 6: By definition of an angle bisector, AD is congruent to DB.
Step 7: By definition of an angle bisector, CE is congruent to EB.
Step 8: Since segment AD is congruent to segment DB and segment CE is congruent to segment EB, we can use the transitive property of equality to state that segment AD is congruent to segment CE.
Step 9: Therefore, segment AD is congruent to segment CE in the given triangle.

Note: The specific triangle or diagram given in the question is not mentioned, so we assume a general triangle with vertices A, B, and C.

Answer 3

To prove that segment AD is congruent to segment CE, we can use the given information and apply geometric reasoning. Here's the step-by-step explanation:

Step 1: Given the triangle ABC, we are given that segment AB is congruent to segment CB. This can be written as AB ≅ CB.

Step 2: We are also given that segment FD bisects segment AB. This means that FD divides AB into two equal segments, which we can denote as AF and FB. So, we have AF ≅ FB.

Step 3: Similarly, we are given that segment FE bisects segment CB. This means that FE divides CB into two equal segments, which we can denote as EC and CF. So, we have EC ≅ CF.

Step 4: We can now compare the segments AD and CE. Since AB ≅ CB and AF ≅ FB, we can combine these equal segments to get AF ≅ CF.

Step 5: Now, using the transitive property of congruence, we can say that AF ≅ CF ≅ EC. (This property allows us to equate any two equal quantities with another equal quantity.)

Step 6: By combining the equal segments AF ≅ CF ≅ EC, we can conclude that AD ≅ CE.

Therefore, we have proved that segment AD is congruent to segment CE based on the given information and the logical steps followed.