The image displays a list of checkboxes for selecting congruent segments and angles. Below is the transcribed text from the image:- □ $ AC \cong YZ $- □ $ AB \cong XY $- □ $ AB \cong YZ $- □ $ \angle B \cong \angle Z $- □ $ \angle A \cong \angle Z $- □ $ \angle C \cong \angle Z $- □ $ CB \cong ZY $- □ $ \angle A \cong \angle X $- □ $ \angle C \cong \angle Y $**Graphs/Diagrams Explanation:**There appears to be part of a grid with a line or shape labeled with letters near it. However, due to the partial view, it is not possible to provide a detailed explanation of the diagram or its context in a geometrical problem. The diagram likely relates to selecting pairs of congruent sides or angles in comparative geometric figures. **Title: Understanding Congruent Triangles on a Coordinate Plane****Introduction:**In this educational exercise, we will explore congruent triangles on a coordinate plane. The focus will be on identifying correct statements about two congruent triangles: $ \triangle ABC $ and $ \triangle XYZ $.**Graph Overview:**The graph displayed consists of two triangles plotted on a coordinate grid, which includes both the x-axis and y-axis. Each triangle is outlined and labeled with specific points.**Triangle $ \triangle ABC $:**- **Vertices:** - $ A $ is located at $ (-4, 0) $ - $ B $ is positioned at $ (-1, 0) $ - $ C $ is at $ (-2, 3) $**Triangle $ \triangle XYZ $:**- **Vertices:** - $ X $ at $ (5, -1) $ - $ Y $ at $ (2, -1) $ - $ Z $ at $ (4, -4) $**Key Concepts:**- Congruent triangles have identical shape and size, but their position and orientation may differ.- Congruency can be proven using various criteria such as Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA).**Conclusion:**By analyzing the points and the properties of these triangles on the coordinate plane, one can ascertain their congruency based on geometric principles. This exercise helps reinforce the understanding of congruent shapes in a coordinate system.

Given that ∆ABC is congruent to ∆XYZOr, ∆ABC≅∆XYZThis means A↔X, B↔Y, C↔Z

Answered: A ABC is congruent to A XYZ. Choose all…

Math

Geometry

A ABC is congruent to A XYZ. Choose all of the correct statements below. C. A -5 4 -3 -2 В -1 -1 Y -2 3 4 5

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Question

The image displays a list of checkboxes for selecting congruent segments and angles. Below is the transcribed text from the image:

- □ $ AC \cong YZ $
- □ $ AB \cong XY $
- □ $ AB \cong YZ $
- □ $ \angle B \cong \angle Z $
- □ $ \angle A \cong \angle Z $
- □ $ \angle C \cong \angle Z $
- □ $ CB \cong ZY $
- □ $ \angle A \cong \angle X $
- □ $ \angle C \cong \angle Y $

**Graphs/Diagrams Explanation:**

There appears to be part of a grid with a line or shape labeled with letters near it. However, due to the partial view, it is not possible to provide a detailed explanation of the diagram or its context in a geometrical problem. The diagram likely relates to selecting pairs of congruent sides or angles in comparative geometric figures.

**Title: Understanding Congruent Triangles on a Coordinate Plane**

**Introduction:**
In this educational exercise, we will explore congruent triangles on a coordinate plane. The focus will be on identifying correct statements about two congruent triangles: $ \triangle ABC $ and $ \triangle XYZ $.

**Graph Overview:**
The graph displayed consists of two triangles plotted on a coordinate grid, which includes both the x-axis and y-axis. Each triangle is outlined and labeled with specific points.

**Triangle $ \triangle ABC $:**
- **Vertices:**
- $ A $ is located at $ (-4, 0) $
- $ B $ is positioned at $ (-1, 0) $
- $ C $ is at $ (-2, 3) $

**Triangle $ \triangle XYZ $:**
- **Vertices:**
- $ X $ at $ (5, -1) $
- $ Y $ at $ (2, -1) $
- $ Z $ at $ (4, -4) $

**Key Concepts:**
- Congruent triangles have identical shape and size, but their position and orientation may differ.
- Congruency can be proven using various criteria such as Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA).

**Conclusion:**
By analyzing the points and the properties of these triangles on the coordinate plane, one can ascertain their congruency based on geometric principles. This exercise helps reinforce the understanding of congruent shapes in a coordinate system.

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