KSU #GSP for HW YES YES YES YES YES YES KSU #GSP for HW YES YES YES YES YES YES YES If you do not have YES next to your student #, either you did not send me GSP constructions or I am waiting for corrections.

1. Construct an angle which is the complement of angle A. B C A  

B C A  

P R

P R P

From HW # 4 A B C D

A B C P Q

A B C P Q

A B C P Q

3.  APQ   BPQ Outline of proof of the construction 1.AP  AQ  BP  BQ 2. PQ  PQ 4.  APQ   BPQ A P Q P B Q M 

M A P Q P B Q 3.  APQ   BPQ 4.  APQ   BPQ Outline of proof of the construction 1.AP  AQ  BP  BQ 2. PQ  PQ 6.  APM   BPM 8.  AMP is supplementary to  BMP 9.  AMP and  BMP are right angles 10. PQ is the perpendicular bisector of AB 5. PM  PM 7.AM  BM,  AMP   BMP 

False True

C B D A 9.In the diagram,  CBD is a right angle, and bisect angles BCD and BDC, respectively. What is the measure of  CAD? 135°

B A C D 12  38  10. In the diagram,, and bisects  ABC. What is the measure of  DBA? 50°

P Q A B C The sum of the measures of the angles of a triangle is 180°. 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 60 o. 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. If the measure of  DCB is 50 , what is the measure of  A? A BC D 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 60 o. 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 60 o. 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? A B C

The sum of the measures of the interior angles of a convex polygon with n sides is (n – 2)180 o.

In this nine sided figure, all 6 diagonals from the same vertex form 7 triangles (9-2). A

The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360 o.

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 60 o. 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)180 o. The sum of the measures of the exterior angles of any convex polygon, …one angle at each vertex, is 360 o.

Practice Problems 1.Find the sum of the measures of  A,  B,  C,  D, and  E A B C D E 40  2.In the diagram, bisects  ABC. What is the measure of  BED? A D B C E 108  96  48 

Practice Problems 1.Find the sum of the measures of  A,  B,  C,  D, and  E A B C D E 40  2.In the diagram, bisects  ABC. What is the measure of  BED? A D B C E 108  96  48  102  460 

3.In the diagram, compute the sum of the angles numbered 1 through 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 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. 720 

A convex polygon with n-sides has.

Homework: Download, print, and complete Homework # 5