1)
Given : In Δ MCG A and I are the midpoint of MG and CG
AI=10.5,
To Find : MC
Solution:
line joining the mid-point of two sides of a triangle is equal to half the length of the third side
A and I are mid points of MG and CG
Hence AI = MC/2
=> 10.5 = MC/2
=> 10.5 x 2 = MC
=> 21 = MC
2)
AG+CI=MG
7+8=15
MG is 15
MG is Congruent to GC therefore
15+15=30
so MG+GC=30
3) MG+GC=30
4) x = 3
x = 3AI + 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 are given that A is the midpoint of MG. This means thatWe also know, via segment addition that
We are given that A is the midpoint of MG. This means thatWe also know, via segment addition thatSubstituting MA = AG to the equation gives us
We are given that A is the midpoint of MG. This means thatWe also know, via segment addition thatSubstituting MA = AG to the equation gives usThis means that MG is twice AG. Their ratio is 1:2.
We are given that A is the midpoint of MG. This means thatWe also know, via segment addition thatSubstituting MA = AG to the equation gives usThis 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.
We are given that A is the midpoint of MG. This means thatWe also know, via segment addition thatSubstituting MA = AG to the equation gives usThis 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,
We are given that A is the midpoint of MG. This means thatWe also know, via segment addition thatSubstituting MA = AG to the equation gives usThis 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.
Substituting again gives us.This means that GC is twice GI. Their ratio is 1:2.
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.
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 x
