10/30/02
MATH 104 – Exam 3 Review
Exam 3 will cover sections 4.4 – 6.3 (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 l || m and t 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) – see exercises
Theorems(1-4): If l || m and t 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 l and m are two lines cut by a transversal t with a pair of corresponding angles
congruent, then l || m .
From this postulate, you should be able to prove any of the following four theorems (given as 1).
Theorems(5-8) : If l and m are two lines cut by a transversal t with
5) a pair of congruent alternate interior angles, then l || m .
6) A pair of congruent alternate exterior angles congruent, then l || m .
7) A pair of supplementary interior angles on the same side of the transversal, then l || m .
8) A pair of supplementary exterior angles on the same side of the transversal, then l || m .
I.
Proofs – There will be three proofs each worth 8-10 points. These fall into 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
C) Proving two triangles are similar. 6.2: #19,20,26 6.3: 27,29,32(use Postulate 2 and theorems 5-8
above),35,37(Use postulate 1 and theorems 1-4).
 We had AA, and SAS, SSS for similarity.
 Note, once you have shown that two triangles are similar to each other with the two (AA)or three (SAS,SSS)
correspondences, then you know that the other 4 or 3 parts of the triangles are congruent (angles) or
proportional (sides). We could use CASTC (corresponding angles of similar triangles are congruent) or CSSTP
(corresponding sides of similar triangles are proportional).
Apply the midsegment and midquad theorems from 6.3
II.
Constructions using straightedge and compass– 3 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 theorem. 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
 Utilize properties of quadrilaterals to find angle 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.
IV.
Chapter 6 Miscellaneous
 Be able to solve proportions – 6.1 up to 15
 Use ratios to solve application problems – 6.1: 35 – 49
 Know the difference between congruence and similarity of objects.
 Determine when two triangles are similar (AA, SSS, SAS for similarity) and if they are, be able to determine side
lengths and angle measures. 6.2 – up to 11.
 Know how areas (and volumes) differ in similar objects – how is it related to the ratio of the side lengths. 6.2 - #13
 Use similar triangles to solve application problems – 6.2: 31, 37, 39
 Identify the three similar triangles when an altitude is drawn to the hypotenuse of a right triangle – Theorem 6.9:
Use these similar triangles and proportions to solve 6.3- #9, 11.
 Apply the side-splitting, midsegment, and midquad theorems to solve problems: 3,5,15,19,23,