If you do not have YES next to your student #, either you did not send me
GSP constructions or I am waiting for corrections.
KSU #
GSP for HW 4
KSU #
GSP for HW 4
432043
397469
374787
445707
441983
483280
394078
312014
406936
443837
339238
401035
420456
YES
350057
428483
338465
340871
427222
427055
341525
493249
401794
449724
437486
382516
414398
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
1. Construct an angle which is the complement of angle A.
B

A

C
1. Construct an angle which is the complement of angle A.
P
BB

A

C
C
P
R
P
R
From HW # 4
B
D
A
C
From HW # 4
A
P
B
Q
C
From HW # 4
A
P
B
Q
C
From HW # 4
A
P
B
Q
C
P
A
B
Q
Outline of proof of the construction
P
1. AP  AQ  BP  BQ
2.
PQ  PQ
3.
APQ  BPQ

A
M
B
4. APQ  BPQ
Q
P
P
A
B
Q
Q
Outline of proof of the construction
P
1. AP  AQ  BP  BQ
2.
PQ  PQ
3.
APQ  BPQ

A
M
B
4. APQ  BPQ
5.
PM  PM
Q
6. APM  BPM
P
P
7. AM  BM , AMP  BMP
8. AMP is supplementary to BMP
A
B
9. AMP and BMP are right angles
10. PQ is the perpendicular bisector of AB
Q
Q
7. True or False: The three angles shown at the right
are supplementary.
64
False
47
69
C
8. True or False: Triangle ABC shown is a right triangle.
5x
True
4x
A
C
9. In the diagram, CBD is a right angle, and
x
B
9. In the diagram, CBD is a right angle, CA and DA
bisect angles BCD and BDC, respectively. What is
the measure of CAD?
C
135°
A
B
D
10. In the diagram, BD  DA, and AD bisects ABC.
What is the measure of DBA?
B
50°
12
D
A
38
C
The sum of the measures of the angles of a triangle is 180°.
Q
C
P
B
A
The existence of this parallel is based on Euclid’s fifth postulate,
(the parallel postulate).
Related Corollaries and Theorems
• Through a point outside a line, exactly one perpendicular can be drawn
…to the line.
• If two angles of one triangle are congruent to two angles of another
…triangle, then the third angles are congruent.
• Each angle of an equiangular triangle has measure 60o.
• In a triangle, there can be at most one right angle or one obtuse angle.
• The acute angles of a right triangle are complementary.
Related Corollaries and Theorems
• Through a point outside a line, exactly one perpendicular can be drawn
…to the line.
• If two angles of one triangle are congruent to two angles of another
…triangle, then the third angles are congruent.
• Each angle of an equiangular triangle has measure 60o.
• In a triangle, there can be at most one right angle or one obtuse angle.
• The acute angles of a right triangle are complementary.
In the diagram, ABD  DCA and BD  BC . If the
measure of DCB is 50, what is the measure of A?
D
A
B
C
Related Corollaries and Theorems
• Through a point outside a line, exactly one perpendicular can be drawn
…to the line.
• If two angles of one triangle are congruent to two angles of another
…triangle, then the third angles are congruent.
• Each angle of an equiangular triangle has measure 60o.
• In a triangle, there can be at most one right angle or one obtuse angle.
• The acute angles of a right triangle are complementary.
• If one side of a triangle is extended, then the measure of the exterior
…angle(s) formed is equal to the sum of the measures of the two remote
…interior (non-adjacent interior) angles.
If one side of a triangle is extended, then the measure of the exterior
angle(s) formed is equal to the sum of the measures of the two remote
interior (non-adjacent interior) angles.
One exterior angle at each vertex of ABC is drawn.
What is the sum of the measures of these three angles?
C
A
B
The sum of the measures of the interior angles of a convex polygon
with n sides is (n – 2)180o.
The sum of the measures of the interior angles of a convex polygon
with n sides is (n – 2)180o.
The sum of the measures of the interior angles of a convex polygon
with n sides is (n – 2)180o.
A
In this nine sided figure, all
6 diagonals from the same
vertex form 7 triangles (9-2).
The sum of the measures of the exterior angles of any convex polygon,
one angle at each vertex, is 360o.
Related Corollaries and Theorems
• Through a point outside a line, exactly one perpendicular can be drawn
…to the line.
• If two angles of one triangle are congruent to two angles of another
…triangle, then the third angles are congruent.
• Each angle of an equiangular triangle has measure 60o.
• In a triangle, there can be at most one right angle or one obtuse angle.
• The acute angles of a right triangle are complementary.
• If one side of a triangle is extended, then the measure of the exterior
…angle(s) formed is equal to the sum of the measures of the two remote
…interior (non-adjacent interior) angles.
• The sum of the measures of the interior angles of a convex polygon with
…n sides is (n – 2)180o.
• The sum of the measures of the exterior angles of any convex polygon,
…one angle at each vertex, is 360o.
Practice Problems
B
1. Find the sum of the measures of
A, B, C, D, and E
A
40
C
E
D
B
2. In the diagram, BE bisects ABC.
What is the measure of BED?
A
48
108
96
D
E
C
Practice Problems
B
1. Find the sum of the measures of
A, B, C, D, and E
A
40
460
C
E
D
B
2. In the diagram, BE bisects ABC.
What is the measure of BED?
A
48
108
102
96
D
E
C
3. In the diagram, compute the sum of the angles
numbered 1 through 8.
1
7
5
2
6
8
4
3
4. In quadrilateral ABCD, the measures of angles A, B, C
and D, in that order, form an increasing arithmetic
sequence. Explain why sides AB and CD must be parallel.
3. In the diagram, compute the sum of the angles
numbered 1 through 8.
1
720
7
5
2
6
8
4
3
4. In quadrilateral ABCD, the measures of angles A, B, C
and D, in that order, form an increasing arithmetic
sequence. Explain why sides AB and CD must be parallel.
(n  3)(n)
A convex polygon with n-sides has
.
2
(n  3)(n)
A convex polygon with n-sides has
.
2
Homework:
Download, print, and complete Homework # 5