Complete addition and subtraction sentences with fractions

Learning Objectives Use the definition of congruent segments to set up addition and subtraction sentences with fractions. Solve for an unknown fractional length in a geometric figure by completing a number sentence. Apply the Segment Addition Postulate to verify segment lengths by completing fractional addition sentences. Determine the length of a sub-segment by completing a fractional subtraction sentence. Justify steps in a geometric problem using properties of congruence and the rules of fraction arithmetic. Apply the principle 'Corresponding Parts of Congruent Triangles are Congruent' (CPCTC) to solve problems involving fractional side lengths. How can an architect ensure two decorative beams are perfectly identical if one beam's length is defined by the s...

TermDefinitionExample Congruent SegmentsTwo or more line segments that have the exact same length. If segment AB is congruent to segment CD, we write \(\overline{AB} \cong \overline{CD}\), which implies their measures are equal (AB = CD).If \(\overline{AB} \cong \overline{CD}\) and the length of AB is \(\frac{3}{4}\) inches, then the length of CD must also be \(\frac{3}{4}\) inches. Segment Addition PostulateIf three points A, B, and C are collinear and B is between A and C, then the length of segment AB plus the length of segment BC is equal to the length of the entire segment AC.If AB = \(\frac{1}{2}\) cm and BC = \(\frac{1}{3}\) cm, then the total length AC = \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\) cm. Corresponding PartsIn congruent figures, the sides and angles that are in the sa...

Segment Addition Postulate If B is between A and C, then \(AB + BC = AC\) Use this postulate to set up an addition sentence when you have smaller, adjacent segments that form a larger segment. This is the foundation for combining fractional lengths. Definition of Congruence If \(\overline{AB} \cong \overline{CD}\), then \(AB = CD\) Use this definition to equate the measures of two segments. If one length is a known fraction and the other is an expression, this allows you to create an equation to solve. Subtraction Property of Equality (for Segments) If \(AB + BC = AC\), then \(AC - AB = BC\) Use this property to create a subtraction sentence when you know the total length of a segment and one of its parts, and you need to find the other part.