savannah6833
Answered

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Quadrilateral ABCD and quadrilateral PQRS are similar. The lengths of AB and CD are 15 units each, and the lengths of AD and BC are 10 units
each.
Use the given information to complete the following sentences.
If the length of PQ is 6 units, then the length of PS is
units. If m_ADC is 62° and m_BCDis 118°, then m QRS is

Quadrilateral ABCD And Quadrilateral PQRS Are Similar The Lengths Of AB And CD Are 15 Units Each And The Lengths Of AD And BC Are 10 Units Each Use The Given In class=

Sagot :

CrazyMoosen

Answer:

4, 118 degrees

Step-by-step explanation:

If two figures are similar, then that means that the ratio of any two corresponding sides in those figures will be equal. For example, the top side of the big parallelogram to the left side of the parallelogram will equal the top side of the small parellolgram to the left side of the small parallelogram. We know that the top side of the large parallelogram is 15 units, the left side of the large parallelogram is 10 units, and the top side of the small parallelogram is 6 units. Now, we can setup a proportion, where PS is the left side of the small parallelogram.

[tex]\frac{15}{10}=\frac{6}{PS}[/tex]

Cross-multiplying, we have [tex]15\cdot PS=60[/tex]. Dividing by 15, we have [tex]PS=4[/tex], so the answer to the first dropdown is 4. Now, in similar figures, the angles to similar triangles are congruent, because the value of the side lengths dont affect the angles as long as they are in the same ratio. That means, that the angle we are looking for, angle QRS is congruent to the same angle it corresponds to in the big parallelogram, which is angle BCD. If BCD is 118 degrees, then that means the angle QRS is also 118 degrees.

shubhamchouhanvrVT

The length of PS is 4, and the angle QRS  is 118 degrees.

What is the similarity?

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

If two figures are similar, then that means that the ratio of any two corresponding sides in those figures will be equal. For example, the top side of the big parallelogram to the left side of the parallelogram will equal the top side of the small parallelogram to the left side of the small parallelogram.

We know that the top side of the large parallelogram is 15 units, the left side of the large parallelogram is 10 units, and the top side of the small parallelogram is 6 units. Now, we can set up a proportion, where PS is the left side of the small parallelogram.

15 / 10 = 6 / PS

Ps = 60 / 15 = 4

Cross-multiplying, we have. Dividing by 15, we have, the answer to the first dropdown is 4. Now, in similar figures, the angles to similar triangles are congruent, because the value of the side lengths doesn't affect the angles as long as they are in the same ratio.

That means, that the angle we are looking for, angle QRS is congruent to the same angle it corresponds to in the big parallelogram, which is angle BCD. If BCD is 118 degrees, then that means the angle QRS is also 118 degrees.

To know more about similarities follow

https://brainly.com/question/10713530

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