Question

1. given prove: $overline{kh}congoverline{uf}$

statements reasons

1. $ku = hf$ 1. given
2. $ku=kh + hu$ 2.
3. $hf = hu+uf$ 3.
4. $kh + hu=hu + uf$ 4.
5. $kh = uf$ 5.
6. $overline{kh}congoverline{uf}$ 6.
7. what is reason 2?

given: $ku = hf$
prove: $overline{kh}congoverline{uf}$

Explanation:

Step1: Segment - addition postulate

A line - segment can be written as the sum of its sub - segments. So, if we have a line - segment $KU$, it can be written as the sum of $KH$ and $HU$.

Step2: Segment - addition postulate

Similarly, for line - segment $HF$, it can be written as the sum of $HU$ and $UF$.

Step3: Substitution property

Since $KU = HF$ (given) and $KU=KH + HU$ and $HF = HU+UF$, we can substitute the expressions for $KU$ and $HF$.

Step4: Subtraction property of equality

Subtract $HU$ from both sides of the equation $KH + HU=HU + UF$.

Step5: Definition of congruent segments

If two segments have the same length, they are congruent.

Answer:

1. Segment - addition postulate
2. Segment - addition postulate
3. Substitution property
4. Subtraction property of equality
5. Definition of congruent segments