Question

has three congruent sides.

has two congruent sides.

has zero congruent sides.

sorting triangles by side lengths
all triangles
______ triangles
______ triangles
______ triangles

1. practice: summarizing

fill in the blanks to complete the theorem and its word - equation.
triangle inequality theorem
the sum of the lengths of any two sides of a triangle is ______ than the length
of the third side
(side 1 + side 2) > ______

Explanation:

Step1: Recall Triangle Inequality Theorem

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Mathematically, for a triangle with sides \(a\), \(b\), and \(c\), we have \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Fill in the Blanks

Based on the theorem, the first blank (describing the relationship) should be "greater", the second blank (the side being compared) is "length", and the third blank (the mathematical expression) is "side 3" (or the length of the third side). So the completed theorem and word - equation are: "The sum of the lengths of any two sides of a triangle is greater than the length of the third side \((\text{side }1+\text{side }2)>\text{side }3\)" (or the length of the third side).

Answer:

The sum of the lengths of any two sides of a triangle is \(\boldsymbol{\text{greater}}\) than the length of the third side \((\text{side }1+\text{side }2)>\boldsymbol{\text{side }3}\) (or the length of the third side)