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Use the distance formula to determine if angle ABC is congruent to angle DEF.Select Yes or No for each statement.

Use The Distance Formula To Determine If Angle ABC Is Congruent To Angle DEFSelect Yes Or No For Each Statement class=

Sagot :

Dorsain, this is the solution for option A:

Option A:

Step 1: Let's calculate the distance from A to B, as follows:

d = √0² - -5² + 0² - -7²

d = √5² + 7²

d = √25 + 49

d = √74

d = 8.6 units

Step 2: Let's calculate the distance from B to C, this way:

d = √4² - 0² + -7² - 0²

d = √4² - 7²

d = √16 + 49

d = √65

d = 8.06 units

Step 3: Let's calculate the distance from A to C, as follows:

d = √(4 - -5)² + (-7 - -7)²

d = √9² + 0²

d = √81

d = 9 units

Step 4: Let's calculate the distance from D to E, this way:

d = √(-1 - -6)² + (1 - -6)²

d = √5² + 7²

d = √25 + 49

d = √ 74

d = 8.6 units

Step 5: Let's calculate the distance from E to F, as follows:

d = √(5 - -1)² + (-8 -1) ²

d = √6² + -9²

d = √36 + 81

d = √117

d = 10.81 units

Step 6: Let's calculate the distance from D to F, this way:

d = √(5 - -6)² + (-8 - -6)²

d = √11² + -2²

d = √121 + 4

d = √125

d = 11.18 units

Step 7: We can conclude that only sides AB and DE are congruent, (8.6 units) but the other two sides of triangles ABC and DEF aren't congruent. Therefore, these two triangles are not congruent.

Now you can continue, following steps 1 to 7 to evaluate options B and C.

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