Using a ruler and a pair of compasses construct a quadrilateral ABCD with AB=9cm, BC=10cm, and AB=7.5cm angle ABC=45degrees and angle BAD=135degrees .
What type of quadrilateral is ABCD?
since consecutive angles are supplementary, it could be a parallelogram.
But how can AB be both 9 and 7.5?
Guess you need to fix your typo and see whether parallel sides are congruent.
Using a ruler and a pair of compasses construct a quadrilateral ABCD with AB=9cm, BC=10cm, and AB=7.5cm angle ABC=45degrees and angle BAD=135degrees .
What type of quadrilateral is ABCD
AD =7.5cm
Hi
Please someone should help me
To construct the quadrilateral ABCD, follow these steps:
1. Take a ruler and draw a line segment AB of length 9 cm.
2. From point A, use a compass to draw an arc with a radius of 7.5 cm.
3. From point B, use the compass to draw another arc with a radius of 10 cm, intersecting the previous arc. Let the point of intersection be C.
4. Connect points A and C with a straight line segment.
5. From point A, use the compass to draw an arc with a radius of 9 cm.
6. From point C, use the compass to draw an arc with a radius of 10 cm, intersecting the previous arc. Let the point of intersection be D.
7. Connect points C and D with a straight line segment.
8. Lastly, connect points D and B with a straight line segment.
Now, to determine the type of quadrilateral ABCD, we can analyze its properties:
1. AB = 9 cm and CD = 9 cm, so opposite sides are equal.
2. BC = 10 cm and AD = 10 cm, so opposite sides are equal.
3. Angle ABC = 45 degrees, and angle BAD = 135 degrees.
Based on these properties, we can conclude that quadrilateral ABCD is a kite.
A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. Additionally, opposite angles in a kite are congruent. In this case, we have sides AB = CD, BC = AD, and angles ABC = BAD, confirming that ABCD is a kite.