Question

mixed review
which property of equality or congruence justifies going from the first statement to the second?

1. 3x + 7 = 19

3x = 12

1. 4x = 20

x = 5

1. ∠1 ≅ ∠2 and ∠3 ≅ ∠2

∠1 ≅ ∠3
get ready! to prepare for lesson 3 - 1, do exercises 43 - 48.
refer to the figure at the right.

1. name four points on line t.
2. are points g, a, and b collinear?
3. are points f, i, and h collinear?
4. name the line on which point e lies.
5. name line t in three other ways.
6. name the point at which lines t and r intersect.

see lesson 2 - 5.
see lesson 1 - 2.

Explanation:

Step1: Analyze 40

Subtract 7 from both sides of $3x + 7=19$. By the subtraction - property of equality, $3x+7 - 7=19 - 7$, so $3x = 12$.

Step2: Analyze 41

Divide both sides of $4x = 20$ by 4. By the division - property of equality, $\frac{4x}{4}=\frac{20}{4}$, so $x = 5$.

Step3: Analyze 42

Since $\angle1\cong\angle2$ and $\angle3\cong\angle2$, by the transitive property of congruence, $\angle1\cong\angle3$.

Step4: Analyze 43

Points on line $t$ are $B$, $H$, $C$, and any other point that lies on the line segment or its extension. For simplicity, we can say $B$, $H$, $C$, and an additional point (not labeled in the given part of the line) as four points on line $t$.

Step5: Analyze 44

Points $G$, $A$, and $B$ are not collinear because they do not lie on the same straight - line.

Step6: Analyze 45

Points $F$, $I$, and $H$ are not collinear as they do not lie on the same straight - line.

Step7: Analyze 46

Point $E$ lies on line $AD$.

Step8: Analyze 47

Line $t$ can be named as line $BH$, line $BC$, line $HC$ (among others as long as two points on the line are used).

Step9: Analyze 48

Lines $t$ and $r$ intersect at point $H$.

Answer:

1. Subtraction property of equality
2. Division property of equality
3. Transitive property of congruence
4. $B$, $H$, $C$, (an additional point on line $t$)
5. No
6. No
7. Line $AD$
8. Line $BH$, line $BC$, line $HC$
9. $H$