Ok, this is going to be confusing to write, but I'll do my best...
<=angle
T=perpendicular to (when upside down)
(Write proof in two-column form)
Given: <JMK=<LMK; segment MK T plane P
Prove: segment JK = segment LK
There is a plane (P) and there are two obtuse triangles on top of the plane, with one of their legs the same. One triangle is triangle JMK, and the other is triangle LMK.
I hope this is enough, but it's from the textbook "Geometry" from McDougal Littell/Houghton Mifflin companies, and written by Ray C. Jurgensen, Richard G. Brown, and John W. Jurgensen. It's on page 160, number 10 on the Chapter Review for Chapter 4.
THANK YOU SO MUCH FOR HELPING!!!
If you look on hotmath . com / help / homework / geometry-library.html, it's the 6th book down from the top on the left side. :-)
To make things more clear, the triangles' sides that are the same are the sides directly above the obtuse angle.
To prove that segment JK is equal to segment LK, we can use the fact that <JMK is equal to <LMK and segment MK is perpendicular to plane P. Here's a step-by-step explanation of how to prove it using two-column form:
1. <JMK = <LMK (Given)
2. MK ⊥ plane P (Given)
3. Construct line JL that lies in plane P and passes through point K.
4. Since MK ⊥ plane P, line JL is perpendicular to MK.
5. Triangle JMK ≅ Triangle LMK (Angle-Angle Postulate)
Explanation for step 5: By having <JMK = <LMK (given) and right angles formed by MK with JL and KM with KL (perpendicular lines), we have two angles and one side of both triangles congruent, satisfying the Angle-Angle Postulate.
6. Segment JK = segment LK (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)
Explanation for step 6: This step follows from the fact that corresponding parts of congruent triangles are congruent (CPCTC). Since triangles JMK and LMK are congruent, their corresponding sides JK and LK are also congruent.
By following these steps, we have proven that segment JK is equal to segment LK.