Question

∆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). ____1_____ are congruent. A ___2____ is a single rigid transformation that maps the two congruent triangles.



1- a) triangle ABC and Triangle XYZ

b) triangle ABC and Triangle MNO

c) triangle JKL and Triangle ABC

d) triangle MNO and Triangle XYZ


2- a) reflection

b) dilation

c) rotation

d) translation

Answer 1

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
C----------O
A----------M

Answer 2

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

Explanation:

PLATO