Which statement explains why ABC is congruent to A A'B'C' ?

Mathematics

1 answer:

Firdavs [7]3 years ago

6 0

Answer:

The two given triangles ABC and A'B'C' are congruent by SSS or AA axiom of congruence.

Step-by-step explanation:

Rigid Transformation is a transformation which PRESERVES (keeps it SAME) the LENGTH and the ANGLES in an image and pre- image.

Here, as we can ΔABC goes under Rigid Transformation in to the ΔA'B'C'

⇒Sides AB, BC and AC correspond to the sides A'B',B'C' and A'C' respectively.

Also the ∠A, ∠B and∠C correspond to ∠A', ∠B' and∠C' respectively.

Now, in ΔABC and ΔA'B'C

AB = A'B'

BC = B' C'

AC = A'C'

⇒The two given triangles are congruent by SIDE SIDE SIDE property.

Also, ∠A = ∠A'

∠B = ∠B'

⇒The two given triangles are congruent by ANGLE ANGLE property.

Hence the two given triangles ABC and A'B'C' are congruent by SSS or AA axiom of congruence.

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Cal is measuring temperature changes in four substances over different time periods as part of a school project. Which data show

djyliett [7]

Answer:

C) The third table. K= 5

$C)\frac{10}{2}=\frac{15}{3}=\frac{25}{5}=\frac{40}{8}=k= 5$

Step-by-step explanation:

1) Below there are the missing data:

A proportional relationship through a constant k. It is obtained when we divide:

$k=\frac{y}{x}$

2)In this case, when we divide the temperature (T) by the time (h).

$k=\frac{T}{h}$

3)So, examining the table below we are searching for a ratio k common to all measures (temperatures over hour).

$A) \frac{12}{3}\neq\frac{25}{5}\neq\frac{36}{6}\neq\frac{81}{9}\\B) \frac{22.5}{3}\neq\frac{30}{4}\neq\frac{52.5}{7}\neq\frac{67.5}{8}\\C)\frac{10}{2}=\frac{15}{3}=\frac{25}{5}=\frac{40}{8}=k= 5\\D)\frac{8.5}{2}\neq\frac{22.5}{5}\neq\frac{28.5}{7}\neq\frac{36}{8}$