Question

Use the congruent triangles shown to answer question 6 and 7.

6. A. B. C. D.
7. Side BC is congruent to which side?
A. ZX
B. YX
C. XY
D. YZ
8. in the image below, ABC ~ DEF
What is the length of EF and the measure of A. 27; 41
B. 27; 49
C. 36; 41
D.45; 49
9. What is the missing degree measure of the third angle of the triangle below?
A. 51
B. 58
C. 61
D. 90
10. Translate triangle ABC3 units right and 2 units down.
What are the coordinates for point A?
A. ( -4, -2)
B. ( 0, -2)
C. ( 1, -1)
D. (1, 3)
11. Name the triangles that are classified by sides
A. right, scalene, isosceles
B. scalene, isosceles, equilateral
C. acute, right, obtuse
D. obtuse, isosceles, acute
Plz help

Answer 1

7. YZ
8. 27,49
9. 51
10.c
11. b

Answer 2

Part 7) is the option
`BC=YZ`

Part 8) is the option B
`27;49\°`

Part 9) is the option C
`61\°`

Part 10) is the option C
`(1,-1)`

Part 11) is the option B scalene, isosceles, equilateral

Explanation:

Part 7)

In this problem we know that

`AB=XY`

`BC=YZ`

`AC=ZX`

therefore

`BC=YZ`

Part 8)

we know that

If triangle ABC is similar to triangle DEF

then

the ratio of their corresponding sides are equal and their corresponding angles are equal

In this problem

Applying the Pythagoras theorem

`FE^(2)=FD^(2)-DE^(2)`

substitute the values

`EF^(2)=45^(2)-36^(2)`

`EF=27`

`EF=BC` ------> the triangles are congruent

therefore

`EF=27`

m∠D=
`49\°`

Part 9)

we know that

The sum of the internal angles of a triangle is equal to
`180\°`

so

Let

x------> the third internal angle of the triangle

`90\°+29\°+x=180\°`

solve for x

`x=180\°-119\°=61\°`

Part 10)

we know that

the rule of the translation is

`(x,y)--------> (x+3,y-2)`

the coordinates of the pre-image of point
`A(-2,1)`

Find the coordinates of the image of point A

Applying the rule of the translation

`(-2,1)--------> (-2+3,1-2)`

`(-2,1)--------> (1,-1)`

Part 11)

we know that

An isosceles triangle has two equal sides

An equilateral triangle has three equal sides

A scalene triangle has no equal sides

therefore

the answer is the option B