03/24/03
MATH 104
–
Exam 3 Review
Exam 3 will cover sections 4.4
–
5.5 (inclusive)
. We did omit construction 8 from 5.5 and so those constructions will be omitted
also (#11

14, 20).
In 5.1 and 5.2, you should be familiar with the names and what each of
the following mean:
Postulate 1:
If
and
is a transversal, then corresponding angles are congruent.
From the postulate you should be able to prove any of the following four theorems (given as 1)
–
se
e exercises
Theorems(1

4)
: If
and
is a transversal, then all of the following angle relationships hold
1)
Alternate interior angles are congruent.
2)
Alternate exterior angles are congruent.
3)
Interior angles
on the same side of the transversal are supplementary.
4)
Exterior angles on the same side of the transversal are supplementary.
Postulate 2: (converse of Postulate 1):
If
and
are two lines cut by a tran
sversal
with a pair of corresponding angles
congruent, then
.
From this postulate, you should be able to prove any of the following four theorems (given as 1).
Theorems(5

8)
: If
and
are two lines cut by a transversal
with
5)
a pair of congruent alternate interior angles, then
.
6)
A pair of congruent alternate exterior angles congruent, then
.
7)
A pair of supplementary interior angles on the same side of the transversal, then
.
8)
A pair of supplementary exterior angles on the same side of the transversal, then
.
I.
Proofs
–
Th
ere will be three proofs each worth 8

10 points. These fall into 2 categories.
A)
In a figure with parallel lines, be able to prove angles are congruent or supplementary

use Postulate 1 and
Theorems 1

4. Exercise 39 page 227.
In a figure with certain
angles congruent or supplementary, be able to prove certain lines are parallel
–
use
Postulate 2 and Theorems 5

8. Exercises 35, 36 page 227.
B)
Proving properties of quadrilaterals, or conversely, proving that quadrilaterals with certain properties must be a
______________ (kite, parallelogram, rhombus, trapezoid, isosceles trapezoid)
Example:
Prove that opposite sides of a parallelogram are congruent. (Theorem 5.15)
Prove if the opposite sides of a quadrilateral are congruent, then the quadrilateral is
a
parallelogram. (Theorem 5.17
–
The converse of 5.15)
Note:
To prove a quadrilateral is a parallelogram, it is necessary to show that opposite sides are parallel, so you
will want to use Postulate 2 and Theorems 5

8.
5.3:
#37, 38, 40
5.4
: # 40, 43, 44,
46,49
II.
Constructions
using straightedge and compass
–
4 of them worth 5 points each.
A)
Section 4.4: Know the 6 basic constructions and use them to 1) construct an angle #13,14,17 2) construct an
altitude, median, perpendicular bisector in a triangle 21, 22
, 25
B)
Section 5.5: Construct parallel lines

Construction 7 : #2,
C)
Construct a quadrilateral with certain givens: # 5,7,9,15
III.
Chapters 4, 5 Miscellaneous
Section 4.4
–
Apply the perpendicular bisector theorem #37
Know the names and be able to identify and
determine angles when parallel lines are cut by a transversal. Section
5.1: #1

28.
Know the names and be able to identify and determine angles when parallel lines are cut by a transversal AND
also apply the exterior angle theorem and angle bisector th
eorem. 5.2: 1

23 (Be sure you can explain why using
appropriate names and terms)
Always

Sometimes

Never questions about properties of quadrilaterals. 5.3, 5.4 + properties about Kites (see #40
pg 254)
Utilize properties of quadrilaterals to find ang
le and side measures in figures containing these quadrilaterals. 5.3
–
1

35, 45; 5.4
–
1

37. Again, you should be able to explain why for the true statements
–
show that you know which
properties apply.
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