In triangle mcg, a and i are the midpoints of mg and cg̅, respectively. if ai = 10.5, what is mc?

Learn more about Functions and Inverse Functions

Recommended textbooks for you

Elementary Geometry For College Students, 7e

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

Elementary Geometry for College Students

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Cengage Learning

Elementary Geometry For College Students, 7e

ISBN:9781337614085

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

Publisher:Cengage,

Elementary Geometry for College Students

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Cengage Learning

Please explain how to solve this question

Let's Do this! in . A and I are the midpoints of and . respectively Consider each given information and answer the questions that foliow. 1、 Given: •What is ? *How did you solve for ? 2. Given: • What is GI? * How did you solve for GI? 3. Given: and # What is ? How did you solve for the sum? 4、 Given: and •What is the value of x? * How did you solve for x? # What is the sum of ? Why? 5. Given: • What is the value of y? * How did you solve for y? • How long are and ? Why?

Answer:

x = 3

AI + MC = 21

Step-by-step explanation:

For this problem, refer to the attached image. I tried to draw it based on the description of the triangle.

A midsegement is a segment that connects two midpoints of a triangle. In this problem, AI is a midsegment. There are 2 theorems when it comes to the midsegment of a triangle. These are:

1. The midsegment is half the measure of the third side of the triangle.

2. The midsegment is parallel to the third side of the triangle.

For this problem, we shall prove and use the 1st theorem.

Similar triangles are triangles whose corresponding sides are proportional. Also, all of their corresponding angles are congruent. This means that all the sides share a common ratio. Like triangle congruence, there are theorems and postulates that prove triangle similarity. The symbol used for similarity is ~.

We have two triangles in the figure, ΔMGC and ΔAGI.

We are given that A is the midpoint of MG. This means that

We also know, via segment addition that

Substituting MA = AG to the equation gives us

This means that MG is twice AG. Their ratio is 1:2.

We can do the same thing for the other side of the triangle, GC.

Since I is the midpoint,

Via segment addition,

Substituting again gives us.

This means that GC is twice GI. Their ratio is 1:2.

We now have 2 proportional sides. AG:MG = 1:2 = GI:GC.

Observe ∠AGI and ∠MGC. They are the same angles, and therefore, congruent to each other. The SAS similarity states that: If two sides of a triangle are proportional to two sides of another triangle, and the angle between those 2 sides are congruent, then the two triangles are similar.

We have 2 proportional sides (AGAG:MG = 1:2 = GI:GC) and the congruent included angle ( ∠AGI). So ΔMGC ~ ΔAGI.

We return to back to what it means to be similar. All sides share a common ratio. The ratio of the sides of the triangles is 1:2. This means, the ratio of AI:MC is also 1:2.

This is also known as the midsegment of a triangle theorem.

We can now solve for x

x is equal to 3.

Substituting back to the expressions

The diagonals of a kite have lengths 13 in and 8 in. Find the area of the kite

identify error and correct it and explain it.

For each of the following sequences, right the following

Complete the factor tree by filling in the missing factors brainly

discuss how you can use these problem or situation in your daily life

If m b=41,what is the measure of DXA

Systematic random sampling is used to interview residents in 25% of 80 apartments in a building. The sampling interval would be

5 examples of postulate

Previous

Next

Ask your question