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2 years ago

These triangles are congruent by the triangle congruence postulate [?]

Mathematics

1 answer:

Vinvika [58]2 years ago

5 0

Given:

A figure of two congruent triangles.

To find:

The triangle congruence postulate by which the given triangles are congruent.

Solution:

First label the vertices as shown below.

In triangle ABC and triangle CDA,

$AB\cong CD$ (Given)

$\angle BAC\cong \angle DCA$ (Given)

$AC\cong AC$ (Common side)

The corresponding two sides and their included angle are congruent in both triangles. So, triangles are congruent by SAS congruence postulate.

$\Delta ABC\cong \Delta CDA$ [SAS congruence postulate]

Therefore, the correct option is B.

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Estefani‘s house is at point E (3,-2) and Jasmin’s house is at point J (-5,3). Jasmin’s house is the Mid-point of Estefani’s hou

iren [92.7K]

The formula for midpoint is

( $\frac{x_{1}+x_{2}}{2}$ , $\frac{y_{1}+y_{2}}{2}$ )

Look at the image below to see the line segment of Estefani's (A), Jasmin's (M), and Preston's (B) houses. Keep in mind that the segment shown below is not accurate in regards to how the line segment formed by Estefani's, Jasmin's, and Preston's houses. It is simply there so you can picture the segment better.

In this case:

$x_{1} =3\\x_{2} =unknown\\y_{1} =-2\\y_{2} =unknown$

^^^Plug in these number into the formula given above...

( $\frac{3+x}{2}$ , $\frac{-2 + y}{2}$ )

To find what x is (a coordinate of Preston's house) you must take the x-value part of the midpoint equation ( $\frac{3+x}{2}$ ) and set it equal to the x-value of the midpoint (-5). Then you must solve for x:

$\frac{3+x}{2}$ = -5

3 + x = -5 * 2

3 + x = -10

x = -10 - 3

x = -13

To find what y is (a coordinate of Preston's house) you must take the y-value part of the midpoint equation( $\frac{-2 + y}{2}$ ) and set it equal to the y-value of the midpoint (3). Then you must solve for y:

$\frac{-2 + y}{2}$ = 3

-2 + y = 3 * 2

-2 + y = 6

y = 6 + 2

y = 8

The coordinate of Preston's house is:

(-13, 8)

Hope this helped!

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