Lesson 3 Viable, Valid, Verified Solidify Understanding

Ready

Use a compass and straight edge to perform the desired constructions.

1.

Construct a rhombus on the segment $A B$ that is given below and that has point $A$ as a vertex. Be sure to check that your final figure is a rhombus.

2.

Construct a parallelogram given sides $\overset{―}{X Y}$ and $\overset{―}{Y Z}$ and $∠ X Y Z$ .

3.

Construct a line parallel to $\overset{―}{Q T}$ and through point $R$ .

Set

4.

Parallel Lines Cut by a Transversal

Given: $\overset{\leftrightarrow}{B F} ∥ \overset{\leftrightarrow}{A D}$

Prove: Same side interior angles $∠ 4$ and $∠ 6$ are supplementary.

Verify each proof by determining if it is valid or not. Provide an explanation.

a.

Student A

Statements	Justifications
$\overset{\leftrightarrow}{B F} ∥ \overset{\leftrightarrow}{A D}$	Given
$∠ 2 ≅ ∠ 6$	Corresponding Angles
$m ∠ 2 + m ∠ 4 = 180 °$	Definition Linear Pair
$∠ 2$ and $∠ 4$ are supplementary	Definition Supplementary
$∠ 6$ and $∠ 4$ are supplementary	Substituting congruent angles

Valid

Not Valid

b.

Student B

So, I see that we are given straight lines, and since straight angles are $180 °$ , and supplementary means adding up to $180 °$ the angles on a line must be supplementary, so that means angles on the same side of a line are supplementary so the angles they are seeing are supplementary.

Valid

Not Valid

c.

Student C

When you translate the lines so that point $B$ lands on point $A$ , we know that all of the angles will line up because the lines are parallel, and when you translate, every point moves the same distance so the parallel lines will coincide. And since point $A$ and $B$ are on the same line to start with all of the angles with $B$ as a vertex will coincide with the angles as $A$ as a vertex. So, $∠ 4$ lands on top of $∠ 8$ , which forms a linear pair with $∠ 6$ , so $∠ 4$ and $∠ 6$ are supplementary.

Valid

Not Valid

d.

Student D

Statements	Justifications
$\overset{\leftrightarrow}{B F} ∥ \overset{\leftrightarrow}{A D}$	Given
$∠ 2 ≅ ∠ 3$	Vertical Angles
$∠ 6 ≅ ∠ 3$	Alternate Interior
$∠ 2 ≅ ∠ 6$	Substitution
$m ∠ 2 + m ∠ 4 = 180 °$	Definition Linear Pair
$∠ 2$ and $∠ 4$ are supplementary	Definition Supplementary
$∠ 6$ and $∠ 4$ are supplementary	Substituting Congruent Angles

Valid

Not Valid

Go

Graph each quadratic function and state the vertex.

5.

$y = {(x - 3)}^{2}$

Vertex:

6.

$y = {(x - 3)}^{2} + 2$

Vertex:

7.

$y = 2 {(x - 3)}^{2} + 2$

Vertex:

8.

$y = {(x + 1)}^{2}$

Vertex:

9.

$y = - {(x + 1)}^{2} - 5$

Vertex:

10.

$y = - 0.5 {(x + 1)}^{2} - 5$

Vertex: