Question

1. find vw.

x 2x + 17 u
w 17 + x v
a. 22
b. 11
c. 6
d. 17
21.
a) equilateral
b) scalene
c) isosceles
22.
a) obtuse
b) equiangular
c) acute
d) right
23.
a) acute
b) right
c) equiangular
d) obtuse
24.
a) scalene
b) equilateral
c) isosceles

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - sides are equal. So, $XU = WV$. Given $XU=2x + 17$ and $WV=x + 17$. Set up the equation $2x+17=x + 17$.

Step2: Solve the equation for x

Subtract x from both sides: $2x - x+17=x - x + 17$, which simplifies to $x+17 = 17$. Then subtract 17 from both sides: $x+17-17=17 - 17$, so $x = 0$.

Step3: Find the length of VW

Substitute $x = 0$ into the expression for $VW$ which is $x + 17$. So, $VW=0 + 17=17$.

Step4: Classify triangles

For question 21:

A right - angled triangle has one angle equal to 90 degrees. An equilateral triangle has all sides and angles equal. An isosceles triangle has two equal sides. A scalene triangle has all sides of different lengths. The given triangle has a right - angle, so it is a scalene right - triangle (since the sides are of different lengths), answer is B.

For question 22:

An obtuse triangle has one angle greater than 90 degrees. An equiangular triangle has all angles equal (each angle is 60 degrees). An acute triangle has all angles less than 90 degrees. A right triangle has one angle equal to 90 degrees. The given triangle has an angle greater than 90 degrees, so it is an obtuse triangle, answer is A.

For question 23:

The triangle has two equal sides (marked by the tick marks) and all angles are less than 90 degrees. It is an acute isosceles triangle, answer is A.

For question 24:

An equilateral triangle has all three sides equal. The given triangle has all sides equal, so it is an equilateral triangle, answer is B.

Answer:

1. d. 17
2. B. scalene
3. A. obtuse
4. A. acute
5. B. equilateral