Download 4-4 Using Congruent Triangles: CPCTC

Geometry
Section 6-5:
Trapezoids & Kites
Name______________________
Date_________________
Over the course of the next couple of days, we will learn to verify and use
properties of trapezoids and kites.
Part I. What you know.
Line m and line n are parallel and t is a transversal.
1. What type of angles are 1 and 2?
2. What is the relationship between the
measures of 1 and 2?
3. What is the midsegment of a triangle?
Find the measure of each numbered angle
4.
5.
5.
6.
Part II: Investigation #1
7. What is an isosceles trapezoid?
8. What markings should be on isosceles trapezoid ABCD?
Use isosceles CAT to answer the following questions.
9. What do you know about the angles of
isosceles CAT ? Make the appropriate
markings on the figure.
10. Eyeball the midpoint of CA and label it M.
Eyeball the midpoint of TA and label it N.
11. Draw the midsegment of CAT by connecting
Points M and N.
12. What name can be given to quadrilateral NTCM ? Why?
13. Conclusion: Both pairs of __________ angles in an isosceles trapezoid
are __________________
Investigation #2
14. Plot the following points in the coordinate plane below for isosceles trapezoid ABCD.
A(-2, 0) B(0, 3) C (4, 3) D(6, 0)
15. Use the distance formula to find the length of each diagonal.
( x 2  x1 ) 2  ( y 2  y1 ) 2
AC =
BD =
16. Conclusion: The diagonals of an ISOSCELES TRAPEZOID
are _________________.
Investigation #3
17. What is a kite?
Use Kite KITE to answer the following questions.
18. What markings should be on Kite KITE ?
19. Draw diagonal KT . What type of triangle is
KIT ? What type of triangle is KTE ?
20. Are KIT and KTE congruent to each other?
21. Now draw diagonal IE . Label its intersection with diagonal KT point A.
22. What is the name of IA in relation to KIT ?
23. Does EA have the same relationship with KTE ?
24. What can you conclude about the intersection of KT and IE ?
25. Conclusion: The diagonals of a KITE are ______________________
to each other.
Part III. Wrapping Things Up
26. Is a trapezoid a parallelogram? Why or why not?
27. Is a kite a parallelogram? Why or why not?
28. The properties of an ISOSCELES TRAPEZOID:
- _______ pair of sides are _____________.
- The _____________________ sides are _________________.
- The ___________ angles are __________________.
- ____________________________ angles are _____________________.
- The ___________________ are _______________________.
29. The properties of a KITE:
- Two pairs of ________________ sides are ____________________.
- The ____________________ are _______________________.
Part IV. Using what you know.
30. Find the measure of each angle.
31. Find the value of x.
Find the measures of the numbered angles in each kite.
32.
33.