28.09.2021

Find the angle of rotation for a figure reflected in two lines that intersect to form a 72° -angle.

. 13

Step-by-step answer

02.03.2022, solved by verified expert

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Mathematics
Step-by-step answer
P Answered by Specialist

66 multiplied by 2 so your answer is 132

Mathematics
Step-by-step answer
P Answered by Specialist

66 multiplied by 2 so your answer is 132

Mathematics
Step-by-step answer
P Answered by Specialist
12. C ends up where A is, at (3, 3).
13. Straight across is 180°.
14. Following one point through this translation leads you to triangle KLM.
15. Since P is 3 units right of x = -3, it will end up 3 units left of it, at -6. As it's 4 units down from y = 4, it will end up 4 units above it, at 8. (-6, 8)
16. It appears to be the same as a translation (it's flipped twice and ends up in the same orientation).

Need clarification?
Mathematics
Step-by-step answer
P Answered by Specialist
12. C ends up where A is, at (3, 3).
13. Straight across is 180°.
14. Following one point through this translation leads you to triangle KLM.
15. Since P is 3 units right of x = -3, it will end up 3 units left of it, at -6. As it's 4 units down from y = 4, it will end up 4 units above it, at 8. (-6, 8)
16. It appears to be the same as a translation (it's flipped twice and ends up in the same orientation).

Need clarification?
Mathematics
Step-by-step answer
P Answered by Specialist

A series of translations to map at least two angles of the image to two angles of the pre-image.

Step-by-step explanation:

we have 2 figures: △ABC and △A′B′C′

△A′B′C′ is the dialation of △ABC

we have to prove that the figures are similar using AA similarity

AA = (Angle-Angle)

Option D is correct.

Mathematics
Step-by-step answer
P Answered by Specialist

D)

Step-by-step explanation:

∠CTA because corresponding parts of congruent triangles are congruent.

The definition of congruent triangles says the corresponding parts of congruent triangles are congruent (CPCTC). Since ΔTOP ≅ ΔCAT, ∠TPO corresponds to ∠CTA.

Mathematics
Step-by-step answer
P Answered by PhD

Option B

Step-by-step explanation:

we know that

If two triangles are congruent, then its corresponding sides and corresponding angles are congruent

If triangle  ACB is congruent to triangle PRQ

then

AC≅PR

CB≅RQ

AB≅PQ

∠A≅∠P

∠C≅∠R

∠B≅∠Q

therefore

∠C≅∠R

Because corresponding parts of congruent triangles are congruent

Mathematics
Step-by-step answer
P Answered by PhD

In the given question,

Δ MOP ≅ Δ CUP

so, ∠MPO ≅ ∠CPU

Step-by-step explanation:

As when we write Δ ABC ≅ Δ DEF (1)

it means that the points are taken in such an order that the congruent sides and angles can be easily found from the notation, i.e., if we take sides and angles from the notation of RHS in the same order as those taken from the notation in LHS, then the corresponding sides and angles will be congruent.

e.g., from (1)

∠ACB ≅ ∠DFE

but, ∠ ABC  is not congruent to ∠ EDF

and,

AB ≅ DE but,  AC  is not congruent to EF.

Now, in the given question,

Δ MOP ≅ Δ CUP

so, ∠MPO ≅ ∠CPU

Mathematics
Step-by-step answer
P Answered by Master

D)

Step-by-step explanation:

∠CTA because corresponding parts of congruent triangles are congruent.

The definition of congruent triangles says the corresponding parts of congruent triangles are congruent (CPCTC). Since ΔTOP ≅ ΔCAT, ∠TPO corresponds to ∠CTA.

Mathematics
Step-by-step answer
P Answered by PhD

Option B

Step-by-step explanation:

we know that

If two triangles are congruent, then its corresponding sides and corresponding angles are congruent

If triangle  ACB is congruent to triangle PRQ

then

AC≅PR

CB≅RQ

AB≅PQ

∠A≅∠P

∠C≅∠R

∠B≅∠Q

therefore

∠C≅∠R

Because corresponding parts of congruent triangles are congruent

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