Mathematics, 08.11.2019 06:31, JamesLachoneus

Select the correct answer from each drop-down menu.
aabc has vertices at a(12.8), b(4,8), and ct4, 14).
axyz has vertices at x(6, 6), 114, 12), and 210, 14).
amno has vertices at m14, 16), m(4,8), and 01-2,8).
ajkl has vertices at /14,-2), k[12, 2), and l(20,4).
are congruent.
congruent. a a single ridged transformation that maps two congruent triangles.
triangles.

Answers: 2

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Answers

The correct answer was given: nicoleamor

The correct option for blank 1 is option B and the correct option for blank 2 is option C.

Explanation:

It is given that ∆ABC has vertices at A(12, 8), B(4, 8), and C(4, 14). ∆XYZ has vertices at X(6, 6), Y(4, 12), and Z(10, 14). ∆MNO has vertices at M(4, 16), N(4, 8), and O(-2, 8). ∆JKL has vertices at J(14, -2), K(12, 2), and L(20, 4).

Plot these vertices on a coordinate plane and draw the triangles as shown below figure.

Two triangles are congruent if the both triangle have same corresponding sides and same angles.

From the figure it is noticed that

AB=MN=8

BC=NO=6

$\angle B=\angle N$

By SAS rule ∆ABC and ∆MNO are congruent.

So, the correct option for blank 1 is B.

From the It is clearly noticed the when we rotate the triangle ∆ABC $90^{\circ}$ counterclockwise along point B, we get ∆MNO.

So, the correct option for blank 2 is C.

Select the correct answer from each drop-down menu. ∆abc has vertices at a(12, 8), b(4, 8), and c(4,

The correct answer was given: MacenParisi

Option B is correct.

Rotation.

Step-by-step explanation:

Given ∆ABC has vertices at A(12, 8), B(4, 8), and C(4, 14). ∆XYZ has vertices at X(6, 6), Y(4, 12), and Z(10, 14). ∆MNO has vertices at M(4, 16), N(4, 8), O(-2, 8). ∆JKL has vertices at J(14, -2), K(12, 2), and L(20, 4).

we have to tell the two triangles which are congruent.

From the graph we see

AB=MN=8 units

BC=OM=6 units

∠ABC=∠OMN=90°

By SAS rule, ΔABC≅ΔMNO.

Option B is correct.

By distance formula,

$ON=\sqrt{(16-8)^2+(4+2)^2}=\sqrt{100}=10 units$

$AC=\sqrt{(14-8)^2+(4-12)^2}=\sqrt{100}=10 units$

All the three sides are of same length and the triangles are congruent therefore, the rotation is a single rigid transformation that results into two congruent triangles.

∆abc has vertices at a(12, 8), b(4, 8), and c(4, 14). ∆xyz has vertices at x(6, 6), y(4, 12), and z(

The correct answer was given: dookeyb2

Option C. is correct

Step-by-step explanation:

In the triangle ABC, vertices are A(12, 8), B(4, 8) and C(4, 14)

AB = $\sqrt{(12-4)^{2}+(8-8)x^{2}}=8$

BC = $\sqrt{(4-4)^{2}+(8-14)^{2}}=6$

AC = $\sqrt{(12-4)^{2}+(8-14)^{2})}=10$

In triangle XYZ vertices are X(6,6), Y(4,12) and Z(10, 14)

XY = $\sqrt{(6-4)^{2}+(6-12)^{2}}=2\sqrt{10}$

YZ = $\sqrt{(4-10)^{2}+(12-14)^{2}}=2\sqrt{10}$

XZ = $\sqrt{(10-6)^{2}+(14-6)^{2}}=4\sqrt{5}$

In triangle MNO, vertices are M(4, 16), N(4, 8) and O(-2, 8)

MN = $\sqrt{(4-4)^{2}+(16-8)^{2}}=8$

MO = $\sqrt{(4+2)^{2}+(16-8)^{2}}=10$

NO = $\sqrt{(4+2)^{2}+(8-8)^{2}}=6$

In triangle JKL, vertices are J(14, -2), K(12,2) and L(20, 4)

JK = $\sqrt{(14-12)^{2}+(-2-2)^{2}}=2\sqrt{5}$

KL = $\sqrt{(20-12)^{2}+(4-2)^{2}}=2\sqrt{17}$

JL = $\sqrt{(20-14)^{2}+(4+2)^{2}}=6\sqrt{2}$

Now we compare the sides for the congruence

Since AB = MN = 8

BC = NO = 6

AC = OM = 10

So ΔABC ≅ Δ MNO

Option C. is correct

The correct answer was given: Babycute8279

Triangle ABC and triangle MNO are congruent. A Rotation is a single rigid transformation that maps the two congruent triangles.

Step-by-step explanation:

ΔABC has vertices at A(12, 8), B(4,8), and C(4, 14).

length of AB = √[(12-4)² + (8-8)²] = 8length of AC = √[(12-4)² + (8-14)²] = 10length of CB = √[(4-4)² + (8-14)²] = 6

ΔMNO has vertices at M(4, 16), N(4,8), and O(-2,8).

length of MN = √[(4-4)² + (16-8)²] = 8 length of MO = √[(4+2)² + (16-8)²] = 10length of NO = √[(4+2)² + (8-8)²] = 6

Therefore:

AB ≅ MNAC ≅ MOCB ≅ NO

and ΔABC ≅ ΔMNO by SSS postulate.

In the picture attached, both triangles are shown. It can be seen that counterclockwise rotation of ΔABC around vertex B would map ΔABC into the ΔMNO.

AABC has vertices at A(12, 8), B(4,8), and C(4, 14).

AXYZ has vertices at X(6, 6), Y(4, 12), and Z(

The correct answer was given: andrew5182

The right answer is triangles ABC and MNO. Congruent triangles are triangles that have the same lengths of its three sides. To get the length of each side, use the distance formula with equation:
$d = \sqrt{( x_{2} - x_{1}) ^{2} +( y_{2} - y_{1} )^2 }$

ABC and MNO have the same segment lengths of its correspoding sides:
AB = MN = 8 units
BC = NO = 6 units
AC = MO = 10 units

The correct answer was given: ceeciliaaa13

To get the length of each side,
use the distance formula with equation:
Distance = ((x2-x1)^2+(y2-y1)^2)^0.5
Solving
AB = 8 units   BC = 6 units AC = 10 units
MN =8units    NO = 6 units MO = 10 units
XY = 6.32 units   YZ = 6.32 units XZ = 8.94 units
JK = 4.47 units    KL = 4.47 units JL = 6 units

1 The right answer is the letter b) triangle ABC and Triangle MNO are Congruent triangles
ABC and MNO are triangles that have the same lengths of its three sides.

2 The answer is the letter c) rotation
There is a rotation of 90º about ABC and MNO the origin is B=N
B=N
CO
AM

The correct answer was given: smartperraorwhateva

Triangle ABC and triangle MNO.
Rotation

The correct answer was given: Gheaton6274

∆ABC and ∆MNOrotation 90° about (4, 8)

Step-by-step explanation:

The two triangles that have the same side lengths (3-4-5) are ∆ABC and ∆MNO, hence these are the ones that are congruent. ∆ABC is a 90° clockwise rotation of ∆MNO. They have a shared point at B = N = (4, 8), which is the center of the rotation.

Of course, the rotation could also be described as a CCW rotation of ∆ABC to make ∆MNO.