# Lesson 3 Can You Say It with Symbols? Solidify Understanding

Remember when you write a congruence statement such as

For instance, from the congruence statements above we would know the following:

The segments and angles in each problem are corresponding parts of two congruent triangles. Make a sketch of the two triangles and mark congruent parts. Then identify the congruence pattern that justifies your statement. Finally, write a congruence statement for each pair of triangles represented.

### 1.

#### a.

Sketch of Triangles

#### b.

Congruence pattern

#### c.

Congruence statement

### 2.

#### a.

Sketch of Triangles

#### b.

Congruence pattern

#### c.

Congruence statement

### 3.

#### a.

Sketch of Triangles

#### b.

Congruence pattern

#### c.

Congruence statement

### 4.

#### a.

Sketch of Triangles

#### b.

Congruence pattern

#### c.

Congruence statement

Olivia is studying

Olivia starts to organize her thinking by writing what she knows and the reasons she knows it.

I know

bisects and because I was given that information. I know that

and by definition of bisect. I know that

because they are opposite sides of a rectangle. I know that

by the transitive property.

Olivia realizes that she already has two sets of corresponding sides that are congruent in

I know that all of the angles in

are right angles because is a rectangle. I know that

and are both right angles because they form a linear pair. I know that

and are both right angles because they form a linear pair.

### 5.

Olivia is excited to have two sides and an angle. But she quickly notices that she has SSA, and she knows that is a pattern she can’t depend on. But right triangles are special because if you have two sides of any right triangle, the third side can be found by doing the Pythagorean Theorem. Olivia believes she has her proof idea and begins to write her proof using as many mathematical abbreviations (symbols) as she can. Help Olivia finish her proof.

Given: quadrilateral

Prove:

Statements | Reasons |
---|---|

1. quadrilateral | given |

2. | given |

### 6.

Perform the following transformations on

Reflect

over . Label your new image . What do you notice about the line segments

, , and ? Compare line segments

, , and to , , and . What is the same and what is different about these segments? Translate

down units and right units. Label your new image . What do you notice about the line segments

, , and ? Compare line segments

, , and to , , and . What is the same and what is different about these segments? Translate

down units and reflect it over the -axis. Label your new image . What do you notice about the line segments

, , and ? Compare line segments

, , and to , , and . What is the same and what is different about these segments?