12.11.24 Entry Ticket 7.G.2

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If two sides of a triangle are 7.5 inches and 12 inches, what is the minimum length of the third side?

Back

The minimum length of the third side (x) can be found using the inequality: x > 12 - 7.5, which simplifies to x > 4.5.

Front

If two sides of a triangle are 7.5 inches and 12 inches, what is the maximum length of the third side?

Back

The maximum length of the third side (x) can be found using the inequality: x < 7.5 + 12, which simplifies to x < 19.5.

Front

What inequality represents the range of values for the third side of a triangle with sides 7.5 inches and 12 inches?

Back

x > 4.5 and x < 19.5.

Front

What does it mean if a triangle has sides of lengths 7.5 inches, 12 inches, and 5 inches?

Back

It means that the triangle satisfies the Triangle Inequality Theorem, as 7.5 + 5 > 12, 7.5 + 12 > 5, and 12 + 5 > 7.5.

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

It helps determine whether three given lengths can form a triangle.

Front

How do you determine if three lengths can form a triangle?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side for all combinations.

Front

What is an example of a set of lengths that cannot form a triangle?

Back

Lengths of 2, 3, and 6 cannot form a triangle because 2 + 3 is not greater than 6.

Tags

CCSS.7.G.A.2

Front

What is the relationship between the sides of a triangle and its angles?

Back

In a triangle, the larger the side, the larger the opposite angle.

Tags

CCSS.HSG.CO.C.10

Front

What is the formula for the perimeter of a triangle?

Back

The perimeter of a triangle is the sum of the lengths of all three sides: P = a + b + c.

Tags

CCSS.3.MD.D.8