Answer :

olayemiolakunle65

Answer:

AB = 14 and BC = 17

Step-by-step explanation:

Congruence is a property that shows an equal relation between sides or angles of a given figure or two figures.

From the question, the given conditions are;

BC = AD, AD = 17, DC = 14, and m< 1 = m<2 .

i. Considering the property of congruence of sides,

BC = 17 (∵ BC = AD and AD has been given to equal 17)

i.e BC = AD = 17

ii. Considering the property of congruent angles and sides,

AB = 14 (∵ m<1 = m<2 and DC is 14)

Therefore, AB = 14 and BC = 17.

akposevictor

Using the SAS congruence theorem and the CPCTC theorem:

  • AB = 14
  • BC = 17

What is SAS Congruence Theorem?

Side-angle-side congruence theorem (SAS) states that two triangles that are congruent will have a pair of congruent angles that is "included", and two pairs of congruent sides that are corresponding.

Thus:

BC = AD (given)

m∠1 = m∠2 (given)

AC = CA (reflexive property)

Thus, ΔABC ≅ ΔCDA by ASA congruence theorem.

Therefore, based on the CPCTC theorem, all the corresponding sides of ΔABC and ΔCDA are congruent.

AB = DC = 14 (congruent sides)

BC = AD = 17 (congruent sides)

Thus, using the SAS congruence theorem and the CPCTC theorem:

  • AB = 14
  • BC = 17

Learn more about SAS congruence theorem on:

https://brainly.com/question/2102943

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