MATH SOLVE

8 months ago

Q:
# Help me please. Help me please. Help me please.

Accepted Solution

A:

a)

To be similar triangles have to have equal angles

triangle ZDB'

1)angle Z=90 degrees

triangle B'CQ

1) angle C 90 degrees

angle A'B'Q=90

DB'Z+A'B'Q+CB'Q=180, straight angle

DB'Z+90+CB'Q=180

DB'Z+CB'Q=90

triangle ZDB'

DZB'+DB'Z=180-90=90

DB'Z+CB'Q=90

DZB'+DB'Z=90

DB'Z+CB'Q=DZB'+DB'Z

2)CB'Q=DZB' (these angles from two triangles ZDB' and B'CQ )

3)so,angles DB'Z and B'QC are going to be equal because of sum of three angles in triangles =180 degrees and 2 angles already equal.

so this triangles are similar by tree angles

b)

B'C:B'D=3:4

B'D:DZ=3:2

CQ-?

DC=AB=21

DC=B'C+B'D (3+4= 7 parts)

21/7=3

B'C=3*3=9

B'D=3*4=12

B'D:DZ=3:2

12:DZ=3:2

DZ=12*2/3=8

B'D:DZ=CQ:B'C

3:2=CQ:9

CQ=3*9/2=27/2

c)

BC=BQ+QC=B'Q+QC

BQ' can be found by pythagorean theorem

To be similar triangles have to have equal angles

triangle ZDB'

1)angle Z=90 degrees

triangle B'CQ

1) angle C 90 degrees

angle A'B'Q=90

DB'Z+A'B'Q+CB'Q=180, straight angle

DB'Z+90+CB'Q=180

DB'Z+CB'Q=90

triangle ZDB'

DZB'+DB'Z=180-90=90

DB'Z+CB'Q=90

DZB'+DB'Z=90

DB'Z+CB'Q=DZB'+DB'Z

2)CB'Q=DZB' (these angles from two triangles ZDB' and B'CQ )

3)so,angles DB'Z and B'QC are going to be equal because of sum of three angles in triangles =180 degrees and 2 angles already equal.

so this triangles are similar by tree angles

b)

B'C:B'D=3:4

B'D:DZ=3:2

CQ-?

DC=AB=21

DC=B'C+B'D (3+4= 7 parts)

21/7=3

B'C=3*3=9

B'D=3*4=12

B'D:DZ=3:2

12:DZ=3:2

DZ=12*2/3=8

B'D:DZ=CQ:B'C

3:2=CQ:9

CQ=3*9/2=27/2

c)

BC=BQ+QC=B'Q+QC

BQ' can be found by pythagorean theorem