You can also explore other questions related to parallelograms and geometry. Vertices A, Band C are joined to vertices D, E and F respectively (see figure). Do you want to learn how to find the values of x, y and z in a parallelogram Visit BYJUS and get the answer to this question with detailed steps and diagrams. In ∆ABC and ∆DEF, AB = DE, AB || DE, BC = EF and BC || EF. Show that:ĪBCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD respectively (see figure). In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see figure). Show that (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D. ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.ĭiagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that the diagonals of a square are equal and bisect each other at right angles. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. I'm basing my response here on what has most commonly appeared in the various geometry textbooks I've taught out of.Some More Questions From Circles Chapter If the diagonals of a parallelogram are equal, then show that it is a rectangle. I do hope you realize that it is difficult to know for sure what your book has covered so far, because different texts may treat topics in a slightly different order. However, you should have showed that if the diagonals bisect each other, the quadrilateral is a parallelogram. BUT.the diagonals of a parallelogram are NOT generally congruent, so that would not be an appropriate way to show that this is a parallelogram. And if both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral must be a parallelogram (this should have been proved already).įor #13, in order to verify that this is a parallelogram, you can show that both pairs of opposite angles are congruent. So, for #12, I think you need to say "I constructed a quadrilateral with both sets of opposite sides congruent. I'm guessing that you have already DONE a proof that if both sets of opposite sides of a quadrilateral are congruent, the quadrilateral must be a parallelogram. You can draw a diagonal in such a quadrilateral, and prove the resulting two triangles are congruent, creating some equal alternate interior angles and two sets of parallel lines. The steps you took in the construction created a quadrilateral with both pairs of opposite sides congruent. my scanner is acting up and my webcam can't take a very clear picture. Writing How can you use the construction shown above to construct a rhombus? Lines RS and PQ would need to be congruent, making lines AB and BC congruent. Show that both opposite sides are congruent and show that the diagonals intersect each other.ġ4. Open-ended Problem Describe two different ways to check that ABCD is a parallelogram. black is the question, blue is the type of question and the purple is my answer)ġ3. (I also had the 2 following questions that go with this as well. Writing Explain why ABCD must be a parallelogram. The following is the problem with which this is suppose to go with:ġ2. Draw segment AD and segment CD/ ABCD is a parallelogram. Label the point where the arcs intersect D. The arc should intersect the arc you drew in step 3.ĥ. Draw an arc with center A and radius BCĤ. Construct segment BC congruent to segment RSģ. Construct segment AB congruent to segment PQĢ. Given two segments, construct a parallelogram with sides congruent to the segments.ġ. Even though this seems like a simple problem, I'm only posting it due to lack of being able to follow the steps of the problem myself. could someone possibly tell me a program that would do the same thing that it's asking in the directions (Pictures from the book included). This was a construction thing, but I don't have a compass.
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