Complete the paragraph proof. given: m is the midpoint of pk pk ⊥ mb prove: △pkb is isosceles it is given that m is the midpoint of pk and pk ⊥ mb. midpoints divide a segment into two congruent segments, so pm ≅ km. since pk ⊥ mb and perpendicular lines intersect at right angles, ∠pmb and ∠kmb are right angles. right angles are congruent, so ∠pmb ≅ ∠kmb. the triangles share mb, and the reflexive property justifies that mb ≅ mb. therefore, △pmb ≅ △kmb by the sas congruence theorem. thus, bp ≅ bk because . finally, △pkb is isosceles because it has two congruent sides.

Solution:

Given: M is the midpoint of PK, PK ⊥ MB.

To Prove: △PKB is isosceles It is given that M is the midpoint of PK and PK ⊥ MB.

Proof: In △PKB and △KMB

1. Midpoints divide a segment into two congruent segments, so PM ≅ KM.

2. Since PK ⊥ MB and perpendicular lines intersect at right angles, ∠PMB and ∠KMB are right angles. Right angles are congruent, so ∠PMB ≅ ∠KMB.

3. The triangles share MB, and the reflexive property justifies that MB ≅ MB.

 Therefore, △PMB ≅ △KMB [by the SAS congruence theorem]

     BP ≅ BK  [C P C T]

4. △PKB is isosceles because it has two congruent sides.

21.4 i did it already for s1

step-by-step explanation: