Answer:
Explanation:
When two ratios are equal to each other, we call the equation a "proportion," and we say the elements of the proportion are proportional to each other. Generally, to show segment lengths are proportional, you want so show they are corresponding sides of similar triangles.
Here, the triangles you want to show as being similar are ...
- the triangle containing the numerator sides: ΔEKP
- the triangle containing the denominator sides: ΔEHL
Triangles are similar if corresponding angles have the same measure.
You will notice that each of these triangles includes angle E, and each also has a right angle. Using these two angles, you can claim similarity using the AA postulate (triangles are similar if two angles match).
So, the proof goes something like this:
Statement . . . . Reason
1. LH⊥EH, PK⊥EH . . . . given
2. Angles PKE and LHE are right angles, so congruent . . . . definition of perpendicular
3. ∠E ≅ ∠E . . . . reflexive property of congruence
4. ΔPKE ≅ ΔLHE . . . . AA similarity postulate
5. EK/EH = EP/EL . . . . corresponding sides of similar triangles are proportional