Are you struggling with solving homework problems related to similar figures? Look no further! In this article, we will unlock the secrets of similar figures and provide you with an answer key for Unit 6 Homework 2. Whether you’re a student or a parent trying to assist your child, understanding the concept of similar figures is crucial for success in geometry. Join us as we delve into the principles behind similar figures and uncover the step-by-step solutions to these challenging homework questions. Get ready to unlock your potential and master the world of similar figures!

Similar figures are an important concept in geometry that involves understanding the relationship between shapes that have the same shape but may differ in size. In Unit 6 Homework 2, we explore the topic of similar figures and how to determine their properties. In this article, we will provide you with an answer key for the homework, giving you a clear understanding of how to approach and solve similar figure problems.

Question 1:

In this question, we are given two triangles. Triangle ABC is similar to triangle DEF, and we need to find the value of angle A.

Solution:

To find the value of angle A, we need to look at the corresponding angles in similar figures. Corresponding angles are angles that occupy the same relative position in different shapes. In this case, angle A in triangle ABC corresponds to angle D in triangle DEF.

Since the two triangles are similar, it means their corresponding angles are congruent (equal). Therefore, if angle D measures 40 degrees, then angle A must also measure 40 degrees.

Answer: The value of angle A is 40 degrees.

Question 2:

In this question, we are given a rectangle with dimensions as shown below. We need to find the length of QR.

Solution:

To find the length of QR, we can use a property of similar figures known as corresponding sides. Corresponding sides are sides that are proportional (in ratio) to each other in similar figures.

In this case, since rectangle LMNO is similar to rectangle PQRS, their corresponding sides must be proportional. If we let x represent the length of QR and y represent the length of NO, then we can set up a proportion:

x/y = RS/NO

Plugging in the given values: RS = 8 cm and NO = 14 cm,

x/14 = 8/14

Simplifying the proportion, we get:

x/14 = 4/7

Cross-multiplying and solving for x, we find:

7x = 14 * 4

7x = 56

x = 8

Answer: The length of QR is 8 cm.

Question 3:

In this question, we are given a trapezoid with bases measuring 12 cm and 16 cm. We need to find the length of the shorter leg.

Solution:

To find the length of the shorter leg, we can use a property of similar figures called proportional sides. In a trapezoid, the legs are parallel, which means they are in proportion to each other.

Using this property, we can set up a proportion between the lengths of the legs. Let x represent the length of the shorter leg and y represent the length of the longer leg. The proportion would be:

x/y = shorter base/longer base

Plugging in the given values: shorter base = 12 cm and longer base = 16 cm,

x/y = 12/16

Simplifying the proportion, we get:

x/y = 3/4

Cross-multiplying and solving for x, we find:

4x = 3 * y

Since there is no information given about y in this question, we cannot determine its value precisely. Therefore, it’s not possible to find an exact value for x (the length of the shorter leg) without additional information about y.

Answer: The length of the shorter leg cannot be determined with only the given information.

Summary:

In this article, we discussed how to approach and solve problems related to similar figures. We explored concepts such as corresponding angles and sides, as well as using proportions to find unknown measurements. By applying these techniques to questions like those found in Unit 6 Homework 2 on unlocking similar figures, you can confidently solve problems involving similar figures and deepen your understanding of this important geometrical concept.