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Urgent!!!!!!!!!!

Given that AB/DE = BC/EF = 1/2, complete the statements to show that ā–³ABC ~ ā–³DEF by the SAS similarity theorem.

1st box: congruent, parallel, or perpendicular

2nd box: A and D, B and E, or C and F

3rd box: congruent, supplementary, or vertical

UrgentGiven that ABDE BCEF 12 complete the statements to show that ABC DEF by the SAS similarity theorem1st box congruent parallel or perpendicular2nd box A and class=

Respuesta :

Ashraf82

Answer:

1st box ā‡’ perpendicular

2nd box ā‡’ B and E

3rd box ā‡’ congruent

Step-by-step explanation:

* Lets revise the case SAS of similarity

- SAS similarity : In two triangles, if two sets of corresponding sides Ā 

Ā  Ā are proportional and the included angles are equal then the two Ā 

Ā  Ā triangles are similar.

- Example : In triangle ABC and DEF, if māˆ A = māˆ D and Ā 

Ā  AB/DE = AC/DF then the two triangles are similar by SAS

* Lets solve the problem

- In Ī” ABC and Ī” DEF

āˆµ AB/DE = BC/EF = 1/2

- That means two sets of corresponding sides are proportion

āˆµ AB is a vertical side and BC is a horizontal side

āˆµ DE is a vertical side and EF is a horizontal side

āˆµ Horizontal and vertical lines are perpendicular

āˆ“ AB āŠ„ BC and DE āŠ„ EF

- So angles B and E are right angles by definition of perpendicular

Ā  Ā lines

āˆµ All right angles are congruent

āˆ“ māˆ B = māˆ D

āˆµ The two triangles have two sets of corresponding sides are

Ā  proportion and the included angles are equal then the two

Ā Ā triangles are similar

āˆ“ ā–³ABC ~ ā–³DEF by the SAS similarity theorem

frika

Answer:

1. Perpendicular

2. B and E

3. Congruent

Step-by-step explanation:

Horizontal and vertical lines are always perpendicular. So, the answer for the first gap is PERPENDICULAR.

Line BC is horizontal line, line AB is vertical line, so lines BC and AB are perpendicular and, therefore, angle B is right angle. Line EF is horizontal line, line ED is vertical line, so lines EF and ED are perpendicular and, therefore, angle E is right angle. So, answer for the second option is angles B and E.

Every two right angles are congruent.

Having two pairs of proportional sides and a pair of congruent adjacent angles, you can apply SAS similarity Postulate.

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