Similar Triangles and Slope

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if they have the same shape but different sizes. This means their corresponding angles are equal and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

How do you calculate the slope of a line?

Back

The slope of a line is calculated by the formula: slope (m) = \frac{\text{rise}}{\text{run}}. This represents the change in y over the change in x.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line that rises 3 units for every 1 unit it runs?

Back

The slope is 3, as it can be expressed as \frac{3}{1}.

Tags

CCSS.8.EE.B.5

Front

If a line falls 2 units for every 3 units it runs, what is the slope?

Back

The slope is -\frac{2}{3}, indicating a downward slope.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no rise.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would involve division by zero.

Tags

CCSS.8.EE.B.5

Front

How can you determine if two triangles are similar using their angles?

Back

If two triangles have two corresponding angles that are equal, then the triangles are similar by the Angle-Angle (AA) similarity criterion.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope, meaning they never intersect.

Tags

CCSS.8.EE.B.5

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -\frac{1}{m}.

Tags

CCSS.HSG.CO.A.1

Front

If triangle DEF has a slope of 1 for side EF, what does this indicate about the angle?

Back

A slope of 1 indicates that the angle formed with the horizontal is 45 degrees.

Tags

CCSS.8.EE.B.6