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# Sorry, can someone help me please 2 questions! teacher wont help. Thank you!

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Sorry, is someone able to help with these 2 questions please? I have been at it for a while now but my teacher will not help help me with it. Thank you!

Find the missing angles in the Parallelogram

m < A =         m < F =

m < B =         m < G =

m < C =         m < H =

m < D =         m < I =

m < E =

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Fill in the missing reasons in the following proof.

 Statement Reasons DFGH is a kite DF≅FG 2 FH ⊥ DG 3   Property of a kite m ∠ DPF=90°   m ∠ GPF=90° 4    Perpendicular segments form right angles. ∠DPF≅∠GPF 5 PF ≅ PF 6 △DPF≅△GPF 7 PD  ≅GP 8
JOKERdps  Dec 24, 2017
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There are a multitude of ways to find the missing angle measures in the diagram. I'll just show you my observations.

1) $$m\angle A=121^{\circ}$$

$$\angle A$$ and the angle across from it form vertical angles. Thus, by the vertical angles theorem, they are congruent.

2) $$m\angle B=59^{\circ}$$

$$\angle A$$ and $$\angle B$$ form a linear pair, so the angles are supplementary by the linear pair theorem. If the angles are supplementary, then the sum of the measure of the angles is 180 degrees.

3) $$m\angle C=59^{\circ}$$

$$\angle B$$ and $$\angle C$$ together form vertical angles. As aforementioned, this means that the measure of both angles are equal.

4) $$m\angle D=55^{\circ}$$

It is given info that the figure is a parallelogram, which by definition is a quadrilateral with two pairs of opposite sides parallel. Plus, the unnamed 55 degree angle and $$\angle D$$ can be classified as alternate interior angles. Since this is true, those angles are congruent.

5) $$m\angle E=4^{\circ}$$

The unnamed 121 degree angle, $$\angle D,$$ and $$\angle E$$ are all angles in a common triangle. The triangle sum theorem states that the sum of the measures of the interior angles of a triangle is 180 degrees. We can use this theorem to solve for the remaining angle:

 $$121+m\angle D+m\angle E=180$$ Use the substitution property of equality to substitute in the known value for the measure of the angle D. $$121+55+m\angle E=180$$ Simplify the left hand side as much as possible. $$176+m\angle E=180$$ Subtract 176 from both sides to isolate angle E. $$m\angle E=4^{\circ}$$

I now want you to try to figure out the rest of the angle measures on your own now! See if you can do it.

 Statements Reasons DFGH is a kite 1. Given $$\overline{DF}\cong\overline{FG}$$ 2. Definition of a kite  (A kite is a quadrilateral with 2 pairs of adjacent congruent sides) $$\overline{FH}\perp\overline{DG}$$ 3. Property of a kite $$m\angle DPF=90^{\circ}\\ m\angle GPF=90^{\circ}$$ 4. Perpendicular segments form right angles $$\angle DPF\cong\angle GPF$$ 5. Right Angles Congruence Theorem (All rights angles are congruent) $$\overline{PF}\cong\overline{PF}$$ 6. Reflexive Property of Congruence (Any geometric figure is congruent to itself) $$\triangle DPF\cong\triangle GPF$$ 7. Hypotenuse Leg Triangle Congruence Theorem (Two rights triangles with corresponding hypotenuses and a select leg congruent are congruent triangles) $$\overline{PD}\cong\overline{GP}$$ 8. Corresponding Parts of Congruent Triangle are Congruent (sometimes abridged to CPCTC)
TheXSquaredFactor  Dec 24, 2017
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THANK YOU!!!! you made the problems easy for me to understand! thanks a ton!

JOKERdps  Dec 24, 2017
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Thank you!

TheXSquaredFactor  Dec 24, 2017