Download 4-4 Using Congruent Triangles: CPCTC

Geometry
Section 6-4:
SPECIAL Parallelograms
Name______________________
Date_________________
Over the course of the next couple of days, we will learn,____________________
______________________________________________________________.
Part I. What you know.
1. What is an isosceles triangle?
2. In the isosceles triangle below mark the sides and angles that are congruent?
3. ABC is an isosceles triangle and BD is an altitude.
Explain why we can we conclude that ABD  CBD.
4. Why can we say that AD  CD ? What name would we give to point D?
5. In the isosceles triangle above, BD can also be called a _____________.
Part II: Investigation #1
6. Now let’s look at Rhombus MATH. Draw diagonal MT .
7. What types of triangles are MAT and MHT ? Why?
9. What is the relationship between ATM and AMT ?
10. What is the relationship between HTM and HMT ?
11. Is MAT  MHT ? How?
12. What can we conclude about ATM, AMT, HTM and HMT ?
13. What name can be given to MT now that you know the relationship of the angles?
14. Now draw diagonal AH . Can you make the same conclusion about AH ?
15. Conclusion: The ________________ of a RHOMBUS, __________ opposite
angles.
Investigation #2
16. Let’s take another look at Rhombus MATH. Draw diagonal MT .
17. Now draw diagonal AH and label the intersection of MT and AH point K.
Because a rhombus is a parallelogram, what do you know about diagonals MT and AH ?
18 What name can we give point K ?
19. Because MAT  MHT are _____________ triangles, what names can be given
to AK and HK ?
20. What type of angles are AKT and AKM ?
21. Conclusion: The diagonals of a RHOMBUS are _______________________ to
each other.
Investigation #3
22. Now let’s investigate the rectangle. Plot the following points in the coordinate
plane below.
A(-3, -1) B(-3, 4) C (5, 4) D(5, -1)
23. Use the distance formula to find the length of each diagonal.
( x 2  x1 ) 2  ( y 2  y1 ) 2
AC =
BD =
24. Conclusion: The diagonals of a RECTANGLE are _________________.
Part III Wrapping things up.
25. What are the three types of parallelograms?
26. The properties of PARALLELOGRAMS from Section 6-2:
1. In a parallelogram, opposite ___________ are ____________.
2. In a parallelogram, opposite ___________ are ____________.
3. In a parallelogram, opposite ___________ are ____________.
4. In a parallelogram, same side interior angles are ___________________.
5. In a parallelogram, diagonals ____________ each other.
27. Are the above properties of parallelograms also true for a Rectangle, Rhombus
and a Square? Why or why not?
28, The properties of a RHOMBUS:
- All four sides are _________________.
- The diagonals are _____________________________.
- The diagonals are _____________________________.
29. The properties of a RECTANGLE:
- All four angles are _________________.
- The diagonals are __________________.
30. The properties for a rhombus and a rectangle also true for a square? Why or why
not?
Part IV. Using what you’ve learned.
31. Find the measures of the numbered angles in the rhombus.
32. One diagonal of a rectangle has length 8x + 2. The other diagonal
has length 5x+11. Find the length of each diagonal.