B
Geometry
Assignment #10: Angles & Triangles
Name_____________________
Due: Oct. 24
Directions: Please answer the following questions and make sure you annotate your work
(briefly justify your steps in your work).
1.
In ∆ABC, m

A=71

and the measure of the exterior angle at B is twice m

ACB. Find m

ACB.
2.
Line segment MP is the perpendicular bisector of the side AC of ∆ABC in which
AB=AC. Prove m

APB=2 m

B algebraically.
A
M
P
C

Geometry
Assignment #10: Angles & Triangles
Name_____________________
Due: Oct. 24
3.
In ∆ABC, AB = CB and P and Q are points on the sides CB and AB such that
AC=AP=PQ=QB. Find m

B.
C
P
A
Q
4.
Given the following information:
TW

UW

TWU

40
VW

UWV 56
Find the measures of the angles of

TUV.
T
B
W
U
V

Geometry
Assignment #10: Angles & Triangles
Name_____________________
Due: Oct. 24
5.
Read the following scenario and complete the proof.
In triangle ABC, the bisector of

B meets AC at X. The perpendicular bisector of BX meets BC at Y. Prove XY is parallel to AB.
Given:
Prove:
Diagram:
Statements Reasons

Geometry
Assignment #10: Angles & Triangles
Name_____________________
Due: Oct. 24
6.
Consider

ABC with the measurements below. a =

A = b =
This configuration does not uniquely define

ABC.
Construct (using your compass and straightedge) each of the two triangles that can be formed from this information.
Triangle #1:
Triangle #2:

Geometry
Assignment #10: Angles & Triangles
Name_____________________
Due: Oct. 24
7.
Consider parallel lines l
1
and l
2
, as shown below. l
1 l
2 a.
Construct ΔABC and ΔADE as specified below:
 Construct isosceles ΔABC with AB = AC such that A falls on l
1
and both B and C fall on l
2
.
 Construct isosceles ΔADE with AD = AE such that both D and E fall on l and

DAE is greater than

BAC.
2 b.
Present an argument that ΔABD

ΔACE and justify your reasoning.