Add up to 4 fractions with denominators of 10 and 100

Learning Objectives Apply the principles of fraction addition to determine and verify side lengths in geometric figures. Prove the congruence of two polygons by calculating and comparing side lengths expressed as sums of fractions. Utilize the SSS (Side-Side-Side) congruence postulate where side lengths are derived from adding up to four fractions with denominators of 10 and 100. Translate geometric properties described with decimal notation into fractional form (tenths and hundredths) to facilitate congruence proofs. Construct a logical argument for figure congruence that relies on accurate fractional arithmetic as evidence. Deconstruct a complex geometric problem into a series of precise arithmetic calculations involving fractions. How can an engineer verify that two preci...

TermDefinitionExample Congruent FiguresTwo or more geometric figures that have the exact same size and shape. All corresponding sides and corresponding angles are equal in measure.If Triangle ABC is congruent to Triangle DEF (written as ΔABC ≅ ΔDEF), it means AB = DE, BC = EF, AC = DF, and ∠A = ∠D, ∠B = ∠E, ∠C = ∠F. Corresponding PartsThe sides or angles of two congruent figures that are in the same relative position. The principle 'Corresponding Parts of Congruent Triangles are Congruent' (CPCTC) is a key reason for proving congruence.In the statement ΔPQR ≅ ΔXYZ, side PQ corresponds to side XY, and angle ∠Q corresponds to angle ∠Y. SSS (Side-Side-Side) Congruence PostulateA rule stating that if three sides of one triangle are congruent to the three corresponding sides of anoth...

Conversion to a Common Denominator (100) \frac{a}{10} = \frac{a \times 10}{10 \times 10} = \frac{10a}{100} To add fractions with denominators of 10 and 100, first convert all fractions with a denominator of 10 into an equivalent fraction with a denominator of 100 by multiplying both the numerator and the denominator by 10. Addition of Fractions with a Common Denominator \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} Once all fractions share the same denominator, add the numerators together and place the sum over the common denominator. This rule is the foundation for calculating total side lengths in our geometric proofs. SSS Congruence Postulate Condition If AB = DE, BC = EF, and AC = DF, then \triangle ABC \cong \triangle DEF This is the logical condition we aim to sati...