Mathematics High School

Pls help :(

Clare and Han are discussing how to find the missing lengths. Clare says she is using similarity. Han says he is using the Pythagorean Theorem.

Find the missing sides

Pls Help :(Clare And Han Are Discussing How To Find The Missing Lengths. Clare Says She Is Using Similarity.

Answers

Answer 1

Answer:

similarity

Step-by-step explanation:

look , dude

the two triangles have the following features:

the angle B= angle C = 90 degree

the angle A= the angle F

so  the third angle in the first triangle = the third angle in the second triangle

so you have one condition of similarity which is the three angles are equal

to get the answer for lengths :

ab/fe= constant of proportionality

thus ab/fe=2.5/5=.5

so ac/13=.5 thus ac=6.5

and 6/de=.5 so de=12

Answer 2

Both similarity and Pythagorean theorem can be used to find the missing lengths as AC = 6.5 and DE = 12.

What are Similar Triangles?

Similar triangles are those triangles which has the same shape but different size.

The length of sides and angles are proportional in similar triangles.

Pythagorean theorem states that for a right angled triangle,

Hypotenuse² = Base² + Altitude²

AC² = BC² + AB²

AC² = 6² + 2.5²

AC² = 42.25

AC = √(42.25) = 6.5

Similarly,

DF² = DE² + EF²

13² = DE² + 5²

DE² = 13² - 5²

DE² = 144

DE = √(144) = 12

If we are using the concept of similarity, ratio of corresponding sides are equal for similar triangles.

AB / EF = BC / DE = AC / DF

2.5 / 5 = 6 / DE = AC / 13

Consider 2.5 / 5 = 6 / DE

Then DE = (6 × 5) / 2.5 = 12

Consider AB / EF = AC / DF

2.5 / 5 = AC / 13

AC = (2.5 / 5) × 13 = 6.5

Hence the missing lengths are AC = 6.5 and DE = 12.

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