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Graded Assignment: Geometry Semester A - Part 2Skyla JonesMs. DykstraGeometryDecember 23, 20201.Write a two-column proof for the following conjecture. You may not need to use all of the rows of the two-column table provided below. You may also add additional rows if needed. Given: Prove: parallelogram ABCD triangle A and B are supplementary. triangle B and C are supplementary.Answer:Statement ReasonParallelogram ABCDGivenAB||DC and AD||BCOpposite sides of a parallelogram are equal∠A and ∠B are same side interior angles and ∠B and ∠C are same side interior angles.Definition of parallelogramm∠A+m∠B=180° and m∠B+m∠C=180° Same side angles of a parallelogram are of 180°∠A and ∠B are supplementary and ∠B and ∠C are supplementaryDefinition of supplementary angles.
Graded Assignment: Geometry Semester A - Part 2Skyla JonesMs. DykstraGeometryDecember 23, 20202.Using a straightedge and compass, construct the perpendicular bisector of FGAnswer:
Graded Assignment: Geometry Semester A - Part 2Skyla JonesMs. DykstraGeometryDecember 23, 20203.Use the following image to answer the questions.(a) How are the triangles similar? Justify your answer with a theorem or postulate.(b) What is the value of x? Show your workAnswer:(a.) In this problem, the triangles presented are congruent. Using the AAA (angle-angle-angle) theorem of similarity, we can prove this. This states that if a triangle's three angles are equal, thenthe triangle's sides are proportional. The three angles of these triangles are considered to be the same, since the picture shows angle A = angle P, and angle B = angle Q, thus angle C = angle R.(b.)(3x + 6)/24 = 28/323x + 6 = (28/32) (24)3x = 21 - 6x = 15/3x = 5