5. Midline Theorem
Midsegment Theorem of
Trapezoid
Theorems on Isosceles
Trapezoid
Theorems on Kite
6. Learning Outcomes
At the end of the lesson, the learners
are able to:
1. Prove the Midline Theorem;
2. Prove the midsegment theorem on
Trapezoids;
3. Prove theorem on Isosceles
Trapezoids;
4. Prove theorem on Kites; and
5. Apply the midline theorem, and
theorems on trapezoids and kites
in solving a problem.
8. It’s Parallelogram! Choose a third side of a triangle.
Mark each midpoint of the other
two sides then connect the
midpoints to form a segment.
Does the segment drawn look
parallel to the third side you
chose?
YES
A
C B
2
3
1
9. It’s Parallelogram!
Measure the segment drawn and
the third side you chose.
Compare the length of the
segment drawn and the third
side you chose.
What did you observe?
The midsegment is half the
length of the third side and
two sides are parallel.
2 u
4 u
A
D E
C B
10. It’s Parallelogram! Cut the triangle along the
segment drawn.
What two figures are formed
after cutting the triangle along
the segment drawn?
Isosceles Trapezoid and
A
D E
C B
11. It’s Parallelogram!
Reconnect the triangle with other
figure in such a way that their
common vertex was midpoint
and that congruent segments
formed by a midpoint coincide.
After reconnecting the cutouts,
what new figure is formed?
Parallelogram
D
E
A
C
B
12. The segment that joins the midpoints of two sides of a
triangle is parallel to the third side and half as long.
Midline Theorem
13.
14. The segment joining the midpoints of the legs of a trapezoid is called
median. The median of a trapezoid is parallel to each base and its
length is one half the sum of the lengths of the bases.
Midsegment
Theorem of
Trapezoid
15.
16. There are three theorems related to isosceles trapezoids as follows:
1. The base angles of an isosceles trapezoid are congruent.
2. Opposite angles of an isosceles trapezoid are supplementary.
3. The diagonals of an isosceles trapezoid are congruent.
Theorems on
Isosceles Trapezoid
17.
18. There are two theorems related to kites as follows:
1. In a kite, the perpendicular bisector of a least one diagonal is the
other diagonal.
2. The area of a kite is half the product of the lengths of its diagonals.
Theorems
on Kite
19.
20. GO FOR IT!
LEARNING TASK
Instructions: Consider each given information and
answer the questions that follow.
25. Summary
1. The Midline Theorem
2. The midsegment theorem on
Trapezoids
3. Theorem on Isosceles Trapezoids
4. Theorem on Kites; and
5. Apply the midline theorem, and
theorems on trapezoids and kites
in solving a problem
