Question

given: $overline{ab}congoverline{cd}$ prove: $overline{ac}congoverline{bd}$ complete the proof. statements: 1. $overline{ab}congoverline{cd}$ 2. $ab = cd$ 3. $ab+bc=bc + cd$ 4. $ab + bc=ac$, $bc + cd=bd$ 5. $ac = bd$ 6. $overline{ac}congoverline{bd}$ reasons: 1. given 2. definition of congruence 3. select choice 4. select choice 5. addition property of equality 6. definition of congruence

Explanation:

Step1: Given information

We are given that $\overline{AB}\cong\overline{CD}$.

Step2: Use congruence - definition

Since $\overline{AB}\cong\overline{CD}$, by the definition of congruence, $AB = CD$.

Step3: Segment - addition postulate

By the segment - addition postulate, $AB + BC=AC$ and $BC + CD = BD$.

Step4: Substitution

Since $AB = CD$, we can substitute $AB$ for $CD$ in the equation $BC + CD=BD$ to get $AB + BC=BD$. And since $AB + BC = AC$, we have $AC=BD$.

Step5: Use congruence - definition again

By the definition of congruence, if $AC = BD$, then $\overline{AC}\cong\overline{BD}$.

Answer:

1. Segment - addition postulate; 4. Substitution Property of Equality