Find and then compare lengths of segments. The vertices of K A T and I E S are K(3,-1), A(2,6),

Name: Problem 30, Chapter 13: McDougal Littell Jurgensen Geometry : Student Edition 2000
Uploaded: 2019-08-24T02:30:23-08:00
Duration: 2 min 45 s
Channel: Luca Alexander
Description: Find and then compare lengths of segments. The vertices of K A T and I E S are K(3,-1), A(2,6), T(5,1) I(-4,1), E(-3,-6), and S(-6,-1) . What word best describes the relationship between K A T and I E S ?

step 1 So for this problem, we are given two line segments, EF in which E, which E is equal to 1 .4, an

Question

Find and then compare lengths of segments. The vertices of $\triangle K A T$ and $\triangle I E S$ are $K(3,-1), A(2,6), T(5,1)$ $I(-4,1), E(-3,-6),$ and $S(-6,-1) .$ What word best describes the relationship between $\triangle K A T$ and $\triangle I E S ?$

   Find and then compare lengths of segments.
The vertices of $\triangle K A T$ and $\triangle I E S$ are $K(3,-1), A(2,6), T(5,1)$ $I(-4,1), E(-3,-6),$ and $S(-6,-1) .$ What word best describes the relationship between $\triangle K A T$ and $\triangle I E S ?$

McDougal Littell Jurgensen Geometry : Student Edition 2000

Ray C. Jurgensen,… 1st Edition

Chapter 13, Problem 30

Instant Answer

Solved by Expert Luca Alexander

08/24/2019

Step 1

The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. - Length of $KA$: \[ \sqrt{(2 - 3)^2 + (6 + 1)^2} = \sqrt{(-1)^2 + (7)^2} = \sqrt{1 + 49} = \sqrt{50} = 5\sqrt{2} \] - Length of $AT$: Show more…

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Find and then compare lengths of segments. The vertices of $\triangle K A T$ and $\triangle I E S$ are $K(3,-1), A(2,6), T(5,1)$ $I(-4,1), E(-3,-6),$ and $S(-6,-1) .$ What word best describes the relationship between $\triangle K A T$ and $\triangle I E S ?$

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Key Concepts

Distance Formula

The distance formula is used in coordinate geometry to determine the length of a segment between two given points. By applying the formula ?[(x? - x?)² + (y? - y?)²], one can calculate the lengths of sides of geometric figures, which is crucial for comparing shapes and establishing properties like congruence.

Triangle Congruence

Triangle congruence refers to the condition when two triangles are identical in shape and size, meaning all corresponding sides and angles are equal. Congruent triangles can be mapped onto each other via rigid transformations such as translations, rotations, and reflections.

SSS Congruence Criterion

The Side-Side-Side (SSS) congruence criterion states that if all three pairs of corresponding sides of two triangles are equal in length, then the triangles are congruent. This criterion provides a straightforward method to verify congruence through side-length comparisons.

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