Question

1.1.8 check your understanding
which of the following statements demonstrates the substitution property?

• (mangle{jkl}=mangle{jkl})
• if (angle{jkl}congangle{qrs}) and (angle{qrs}congangle{def}), then (angle{jkl}congangle{def})
• if (mangle{abc}=mangle{jkl}), then (mangle{jkl}=mangle{abc})
• if (mangle{jkl}+mangle{def}=mangle{qrs}) and (mangle{def}=30^{circ}), then (mangle{jkl}+30^{circ}=mangle{qrs})

Explanation:

The substitution property states that if one quantity equals another, then the first quantity can be substituted for the second in any expression or equation. In the option "If \(m\angle JKL + m\angle DEF=m\angle QRS\) and \(m\angle DEF = 30^{\circ}\), then \(m\angle JKL+30^{\circ}=m\angle QRS\)", the value of \(m\angle DEF\) (which is \(30^{\circ}\)) is substituted into the first - equation. The first option is the reflexive property (\(a = a\)), the second is the transitive property for congruent angles (\(\angle A\cong\angle B\) and \(\angle B\cong\angle C\) implies \(\angle A\cong\angle C\)), and the third option has an incorrect form of substitution as there is no given equality to support the substitution.

Answer:

If \(m\angle JKL + m\angle DEF=m\angle QRS\) and \(m\angle DEF = 30^{\circ}\), then \(m\angle JKL+30^{\circ}=m\angle QRS\)