# Lesson 1

Lines, Angles, and Curves

### Problem 1

Find the values of $$x, y,$$ and $$z$$.

### Problem 2

Give an example from the image of each kind of segment.

1. a diameter
2. a chord that is not a diameter

### Problem 3

Identify whether each statement must be true, could possibly be true, or definitely can’t be true.

1. A diameter is a chord.
2. A radius is a chord.
3. A chord is a diameter.
4. A central angle measures 90$$^\circ$$.

### Problem 4

Write an equation of the altitude from vertex $$A$$.

### Solution

(From Unit 6, Lesson 17.)

### Problem 5

Triangle $$ABC$$ has vertices at $$(5,0), (1,6),$$ and $$(9,3)$$. What is the point of intersection of the triangle’s medians?

A:

The medians do not intersect in a single point.

B:

$$(3,3)$$

C:

$$(5,3)$$

D:

$$(3,4.5)$$

### Solution

(From Unit 6, Lesson 16.)

### Problem 6

Consider the parallelogram with vertices at $$(0,0), (8,0), (4,6),$$ and $$(12,6)$$. Where do the diagonals of this parallelogram intersect?

### Solution

(From Unit 6, Lesson 15.)

### Problem 7

Lines $$\ell$$ and $$p$$ are parallel. Select all true statements.

A:

Triangle $$ADB$$ is congruent to triangle $$CEF$$.

B:

The slope of line $$\ell$$ is equal to the slope of line $$p$$.

C:

Triangle $$ADB$$ is similar to triangle $$CEF$$.

D:

$$\sin(A) = \sin(C)$$

E:

$$\cos(B) = \sin(C)$$

### Solution

(From Unit 6, Lesson 10.)

### Problem 8

Mai wrote a proof that triangle $$AED$$ is congruent to triangle $$CEB$$. Mai's proof is incomplete. How can Mai fix her proof?

We know side $$AE$$ is congruent to side $$CE$$ and angle $$A$$ is congruent to angle $$C$$. By the Angle-Side-Angle Triangle Congruence Theorem, triangle $$AED$$ is congruent to triangle $$CEB$$.