Answer:
10.5 ft
Step-by-step explanation:
In ΔQRS,
- m∠S=90°
- m∠R=29°,
- SQ = 5.8 feet.
See the diagram below.
The triangle is a Right Triangle,
Using trigonometric ratios,
Terra writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a
parallelogram:
Terra's proof
1. AO = OC because it is given that diagonals bisect each other.
2. BO = OD because it is given that diagonals bisect each other.
3. For triangles AOB and COD, angle 1 is equal to angle 2 as they are
4. Therefore, the triangles AOB and COD are congruent by SAS postulate.
5. Similarly, triangles AOD and COB are congruent.
6. By CPCTC, angle ABD is equal to angle BDC and angle ADB is equal to angle DBC.
7. As the alternate interior angles are congruent the opposite sides of quadrilateral ABCD are parallel
8. Therefore, ABCD is a parallelogram.
Which is the missing phrase in Terra's proof? (6 points)
alternate interior angles
Oь
corresponding angles
same-side interior angles
d
vertical angles
Terra's proof
1. AO = OC because it is given that diagonals bisect each other.
2. BO = OD because it is given that diagonals bisect each other.
3. For triangles AOB and COD, angle 1 is equal to angle 2 as they are
4. Therefore, the triangles AOB and COD are congruent by SAS postulate.
5. Similarly, triangles AOD and COB are congruent.
6. By CPCTC, angle ABD is equal to angle BDC and angle ADB is equal to angle DBC.
7. As the alternate interior angles are congruent the opposite sides of quadrilateral ABCD are parallel
8. Therefore, ABCD is a parallelogram.
Which is the missing phrase in Terra's proof? (6 points)
alternate interior angles
Oь
corresponding angles
same-side interior angles
d
vertical angles
2 answers:
You might be interested in
Answer:
x = 56
Step-by-step explanation:
Since two sides of the triangle have the same length, we knows it's isosceles. This means we we will have two base angles with the same value. Since x is the angle in between both legs, we knows x is the vertex angle.
62 is a base angle, which means the other base will be 62 as well. And since the angles of a triangle always add up to 180,
x = 180 - (62 + 62)
x = 180 - 124
x = 56
