Answer:
3. m<GHF= 90 degrees
4. m<DGH= 45 degrees
5. HF=5
6. DE=50
Step-by-step explanation:
3. The measure of angle DGF and EFG are 45 degrees each and 45+45 is 90 degrees. When you subtract 90 from 180, you get 90.
4. A square is also a rectangle and a rectangle has four right angles and it is a rhombus and the diagonals bisect the angles. This means that angle DGH is half of angle DGF and 90/2=45.
5. The diagonals of a square are congruent so it is also 5.
6. You use the Pythagorean Theorem and 5^2 + 5^2=50
The diagonals of square DEFG intersect at H. The measure of the following option; 3. m∠GHF= 90 degrees. 4. m∠DGH= 45 degrees 5. HF=5 6. DE=50
That rectangle whose all sides are equal is called a square.
A square is always a rectangle, parallelogram, a rhombus, and a quadrilateral but its reverse statement may or may not be true.
(ie it is not always necessary that a rectangle is a square or a parallelogram is a square or a rhombus is a square).
The diagonals of square DEFG intersect at H.
Given that EH = 5, we need to find the measure of the following option;
3. The measure of ∠DGF and ∠EFG are 45 degrees each .
The sum of the angle of the bisector of diagonal 45 + 45 = 90 degrees.
When you subtract 90 from 180, you get 90.
4. A square is also a rectangle and a rectangle has four right angles and it is a rhombus and the diagonals bisect the angles.
This means that ∠DGH is half of ∠DGF
90/2 = 45.
5. The diagonals of a square are congruent so HF is 5.
6. By Pythagorean Theorem
[tex]DF^2 = 5^2 + 5^2\\\\DF = \sqrt{50}[/tex]
Learn more about Pythagoras theorem here:
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