Is there a relation between PM and MO? Are the congruent angles between congruent sides?
See solution.
Practice makes perfect
Before making a paragraph proof, let's draw the two triangles shown in the figure and mark the corresponding congruent parts.
Since △ MOP is equilateral, we get that PM≅ MO≅ PO.
Let's summarize all the congruent parts of both triangles.
cc
LP ≅ NO & Side
∠LPM ≅ ∠NOM & Included Angle
PM ≅ OM & Side
By applying the Side-Angle-Side (SAS) Congruence Postulate we conclude △ LMP ≅ △ NMO.
Completed Proof
Given: & LP ≅ NO, ∠LPM ≅ ∠NOM and
& △ MOP is equilateral
Prove: & △ LMP ≅ △ NMO
Proof: Since △ MOP is equilateral, we get PM≅MO. Then, two sides and the included angle of △ LMP are congruent to two sides and the included angle of △ NMO. By the Side-Angle-Side (SAS) Congruence Postulate we conclude △ LMP ≅ △ NMO.
