Given MPRK is a parallelogram, how would you prove, in two-column format, that the measure of angle MTK = measure of angle PMT + measure of angle RKT?

Answer 1

I assume, point #T# is any point inside of parallelogram.
See below the proof.

Draw a line through point #T# parallel to sides #MP# and #KR# of a parallelogram #MPRK#. Let's assume that it intersects side #KM# at point #X#.
Statement: #m/_PMT = m/_MTX# Reason: Angles #/_PMT# and #/_MTX# are alternate interior angles with parallel lines #MP# and #TX# and transversal #MT#.
Statement: #m/_KTX = m/_RKT# Reason: Angles #/_KTX# and #/_RKT# are alternate interior angles with parallel lines #KR# and #TX# and transversal #KT#. Hence, they have the same measure.
Statement: #m/_PMT + m/_RKT = m/_MTX + m/_KTX# Reason: Above equalities of corresponding measures.
Statement: #m/_PMT + m/_RKT = m/_MTK# Reason: # m/_MTX + m/_KTX = m/_MTK#

End of proof.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2
StatementsReasons
MPRK is a parallelogram.Given
MK is parallel to PR.Definition of a parallelogram
Angles MTK and PMT are alternate interior angles formed by transversal KT and parallel lines MK and PR.Alternate Interior Angles Theorem
Angles MTK and RKT are corresponding angles formed by transversal KT and parallel lines MK and PR.Corresponding Angles Theorem
Angle PMT is congruent to angle RKT.Corresponding Angles Theorem
Therefore, measure of angle MTK = measure of angle PMT + measure of angle RKT.Angle Addition Postulate
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7