We are asked to determine the area of the given figure. To do that we will divide the figure into a square and a triangle. The area of the square is the product of its dimension, therefore, the area is:
The area of the triangle is given by the following formula:
Where "b" is the base and "h" is its height. Replacing the values:
The total area is the sum of both areas:
replacing the areas:
Answer: yes it can be a measure of a triangle
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Sides: a = 6 b = 11 c = 13
Area: T = 32.863
Perimeter: p = 30
Semiperimeter: s = 15
Answer:
∠EGB and ∠AGF are congruent;
Transitive Property of Equality
Step-by-step explanation:
The vertical angles theorem is about the angles that are opposite to each other. These angles are formed when two lines cross each other
Vertical angles are congruent i.e their measures are equal
Look at the attached graph
Given:
AB // CD
E , G , H , F are col-linear
The line which contains points E , G , H , F is a transversal for the parallel lines AB and CD
∵ AB and EF intersected at point G
∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem
When lines AB and EF intersected at G they formed opposite angles like angles EGB and AGF, then angles EGB and AGF are congruent ( vertical angle theorem)
∵ AB // CD and EF is a transversal
∴ m∠AGF = m∠CHF (corresponding angles theorem)
Transitive Property of Equality: if one angle is equal to two other angles, then the two other angles are equal
Therefore, If a = b and b = c, then a = c
∵ m∠EGB = m∠AGF
∵ m∠AGF = m∠CHF
∴ m∠EGB = m∠CHF (transitive property theorem)
∠EGB and ∠AGF are congruent; Transitive Property of Equality
Answer:
The component of orthogonal to
is
.
Step-by-step explanation:
Let and
, from Linear Algebra we get that component of
parallel to
by using this formula:
(Eq. 1)
Where is the norm of
, which is equal to
. (Eq. 2)
If we know that and
, then we get that vector component of
parallel to
is:
Lastly, we find the vector component of orthogonal to
by applying this vector sum identity:
(Eq. 3)
If we get that and
, the vector component of
is:
The component of orthogonal to
is
.