Given: PM || GK, PH || MJ, PH perpendicular PM, PO = MO, <1= <2, PH= 1/5 PM Prove: JK= 1/5 PM

Question

Given diagram is triangle GOK (with base GK). Inside triangle is a figure (looks like a rectangle but not given that it is), quadrilateral HPMJ (labelled clockwise in that order starting from bottom left. Within the figure, triangle POM, has base PM and the base angles are labelled angles 1 and 3(<P is 1 and <M is 3). angle 4 is angle KMJ. 

Answer 1

Jennifer,

 

I can't answer this without knowing what angle two is but here is the approach.

 

1) show triangles POM and GOK are similar because their angles are complementary (PM parallel to GK).

 

2) POM is iscoceles so GOK is too. This means PG equals MK.

 

3) show triangles PGH and MKJ are similar. This requires angle 2 I think.

 

4) show those triangles are iscoceles too. Now PH, JK, GH, and MK are equal. 

 

5) PH=PM/5=JK.

 

Since it's give as a hint, angle two is critical to this proof, so watch step 3 carefully. Hope that helps!