Step 1
Find the measure of the vertex angle and the base angle
we know that
An isosceles triangle has two equal sides and two equal angles
The two equal angles are called the base angle
The third angle is called the vertex angle
Let
Y------> the vertex angle
X-----> the base angle
Z----> the base angle
[tex]Z=X[/tex] ------> equation A
Remember that
The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
so
[tex]X+Y+Z=180\°[/tex] -----> equation B
In this problem
The measure of the vertex angle, Y, is twice the measure of a base angle
[tex]Y=2X[/tex] -----> equation C
Substitute equation A and equation C in equation B
[tex]X+[2x]+[x]=180\°[/tex]
Solve for X
[tex]4X=180\°[/tex]
[tex]X=45\°[/tex]
so
[tex]Z=X=45\°[/tex]
Find the value of Y
[tex]Y=2X[/tex]
[tex]Y=90\°[/tex]
Step 2
Verify the statements
case A) The measure of angle Y is aright angle
The statement is True
Because, the measure of the vertex angle Y is [tex]90\°[/tex]
case B) The measure of angle Z is [tex]45\°[/tex]
The statement is True
See the procedure in the Step [tex]1[/tex]
case C) The measure of angle X is [tex]36\°[/tex]
The statement is False
Because, the measure of angle X is [tex]45\°[/tex]
case D) The measure of the vertex angle is [tex]72\°[/tex]
The statement is False
Because, the measure of the vertex angle Y is [tex]90\°[/tex]
case E)The perpendicular bisector of creates two smaller isosceles triangles
The statement is True
Because, the perpendicular bisector creates two smaller [tex]45\°-90\°-45\°[/tex] triangles, and we know that a [tex]45\°-90\°-45\°[/tex] triangle is an isosceles triangle
the answer is
The measure of angle Y is aright angle
The measure of angle Z is [tex]45\°[/tex]
The perpendicular bisector of creates two smaller isosceles triangles
Answer:
Your answer is A, B, and D.
Step-by-step explanation:
A- Angle Y is a right angle
B- The measure of angle Z is 46°
D- The perpendicular bisector creates two smaller isosceles triangles.
All three of these statements are true!
