a.
To explain: The reason for the y-coordinate of the point P is
Given information:
The diagram of a unit
Calculation:
The point
b.
To prove: The two triangles shown in the diagram are congruent.
Given information:
The diagram of a unit circle with two points
Calculation:
Name the points of the triangles as shown below.
Observe that the triangles OAQ and OBP are right triangles with hypotenuses OQ and OP respectively.
The angles AOQ and BOP are opposite angles. So, they are equal. Now, since the two angles of the two triangles are equal, the third will also be equal. That means, the triangles are similar.
Since the triangles are similar right triangles with same equal hypotenuses, the triangles are congruent.
c.
To show: The two blue segments are congruent.
Given information:
The diagram of a unit circle with two points
Calculation:
Name the points of the triangles as shown below.
Since triangles are congruent and the angles AOQ and BOP are equal, the sides AQ and BP are equal. That means, the two blue segments are congruent.
d.
To show: The y-coordinate of the point
Given information:
The diagram of a unit circle with two points
Calculation:
The point
The segments AQ and PB are congruent. So, the length PB is also
e.
To conclude:
Given information:
The diagram of a unit circle with two points
Calculation:
From part (a), the y-coordinate of the point
Chapter 14 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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