9. what is the intersection of plane stxw and plane tuyx?
10. write the two conditional statements that make up the following biconditional. a triangle is isosceles if and only if it has two congruent sides.
a. a triangle is isosceles if and only if it has two congruent sides.
a triangle has two congruent sides if and only if it is isosceles.
b. if a triangle is isosceles, then it has two congruent sides.
if a triangle has two congruent sides, then it is isosceles.
c. a triangle is isosceles.
it has two congruent sides.
d. if i drink juice, then it is breakfast time.
a triangle is isosceles only if it has two congruent sides..
11. what is the converse of the following conditional? if a number is a natural number, then it is a whole number.
a. if a number is a natural number, then it is a whole number.
b. if a number is not a whole number, then it is not a natural number.
c. if a number is a whole number, then it is a natural number.
d. if a number is not a natural number, then it is not a whole number.
12. find the midpoint between the points (3, -1) and (8, -6).
a. (-\frac{11}{2}, -\frac{7}{2})
c. (11, -7)
b. (\frac{11}{2}, -\frac{7}{2})
d. (2, -2)
13. name the line and plane shown in the diagram.
a. \overleftrightarrow{nm} and plane po
c. line m and plane mnp
b. \overleftrightarrow{mn} and plane pm
d. \overleftrightarrow{mn} and plane mnp

Question

Accepted Answer

### 9.
# Explanation:
## Step1: Recall plane - intersection property
The intersection of two planes is a line. Identify the common line in plane $STXW$ and plane $TUYX$.
## Step2: Observe the figure
The common line for plane $STXW$ and plane $TUYX$ is $\overleftrightarrow{TX}$.
# Answer:
b. $\overleftrightarrow{TX}$

### 10.
# Explanation:
A biconditional statement “$p$ if and only if $q$” is equivalent to two conditional statements: “if $p$, then $q$” and “if $q$, then $p$”. Here $p$ is “a triangle is isosceles” and $q$ is “it has two congruent sides”.
# Answer:
b. If a triangle is isosceles, then it has two congruent sides. If a triangle has two congruent sides, then it is isosceles.

### 11.
# Explanation:
The converse of a conditional statement “if $p$, then $q$” is “if $q$, then $p$”. Here $p$ is “a number is a natural number” and $q$ is “it is a whole number”.
# Answer:
c. If a number is a whole number, then it is a natural number.

### 12.
# Explanation:
## Step1: Recall mid - point formula
The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
## Step2: Substitute the values
Given $(x_1,y_1)=(3,-1)$ and $(x_2,y_2)=(8,-6)$. Then $\frac{3 + 8}{2}=\frac{11}{2}$ and $\frac{-1+( - 6)}{2}=\frac{-1 - 6}{2}=-\frac{7}{2}$.
# Answer:
b. $(\frac{11}{2},-\frac{7}{2})$

### 13.
# Explanation:
The line is named by two points on the line. Here the line can be named as $\overleftrightarrow{MN}$. The plane is named by three non - collinear points on the plane. Here the plane can be named as plane $MNP$.
# Answer:
d. $\overleftrightarrow{MN}$ and plane $MNP$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

9.

Step1: Recall plane - intersection property

Step2: Observe the figure

Answer:

10.