Kyle is at the end of a pier 30 feet above the ocean. His eye level is 3 feet above the pier. He is using binoculars to watch a
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The triangles are drawn in the picture attached.
Let's call M the intersection point of AB and CD. Since CD is the perpendicular bisector, we know that:
AM ≡ MB (bisector = divides into two equal pieces)
∠AMD ≡ ∠AMC ≡ ∠BMC ≡ ∠BMD (perpendicular = forms 4 angles of 90°)
Considering ΔAMD and ΔBMD, they have also MD in common, therefore, we can use the SAS (side - angle - side) congruency criterium to prove that they are congruent.
Similarly for ΔAMC and ΔBMC.
Therefore, <span>ΔADC ≡ ΔBCD because they are made of congruent triangles.</span>
Hence, with the SAS congruency theorem, we can demonstrate that ΔADC ≡ ΔBCD
Let's call M the intersection point of AB and CD. Since CD is the perpendicular bisector, we know that:
AM ≡ MB (bisector = divides into two equal pieces)
∠AMD ≡ ∠AMC ≡ ∠BMC ≡ ∠BMD (perpendicular = forms 4 angles of 90°)
Considering ΔAMD and ΔBMD, they have also MD in common, therefore, we can use the SAS (side - angle - side) congruency criterium to prove that they are congruent.
Similarly for ΔAMC and ΔBMC.
Therefore, <span>ΔADC ≡ ΔBCD because they are made of congruent triangles.</span>
Hence, with the SAS congruency theorem, we can demonstrate that ΔADC ≡ ΔBCD
Answer:
Step-by-step explanation:
Given:
QSR is a right triangle.
QT = 10
TR = 4
To find:
The value of q.
Solution:
Hypotenuse of QSR = QT + TR
= 10 + 4
= 14
Geometric mean of similar right triangle formula:
Do cross multiplication.
Switch the sides.
Taking square root on both sides.
The value of q is .