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.
2 answers:
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.
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