What additional piece of information would prove DABD ≅ DCBD?

Mathematics

1 answer:

Alekssandra [29.7K]2 years ago

4 0

Answer:

∠BAD ≅ ∠BCD

Step-by-step explanation:

The complete equation is attached.

Two triangles are congruent to each other if all their three sides are equal to each other and all their three angles are equal to each other.

The angle side angle (ASA) congruence theorem states that two triangles are congruent if two angles of one triangle is equal to two angles of the other triangle and also if their included side are equal.

Since AB = BC, ∠ABD = ∠CBD. For ∠ABD ≅ ∠CBD based on ASA then ∠BAD ≅ ∠BCD

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Find the area of the shaded region.

kondor19780726 [428]

The region is made up of

• a right triangle with short leg 10 m and hypotenuse 26 m

• a parallelogram with sides 40 m and 26 m (the 26-m side corresponds to the aforementioned hypotenuse)

• another triangle with two known legs of length 20 m and 26 m

Find the height of the right triangle using the Pythagorean theorem. If the height is h, then

(10 m)² + h² = (26 m)² ⇒ h² = 576 m² ⇒ h = 24 m

This height is common to all three shapes.

Now find the area of each shape.

• right triangle:

1/2 × (10 m) × (24 m) = 120 m²

• parallelogram:

(40 m) × (24 m) = 960 m²

• other triangle:

• 1/2 × (20 m) × (24 m) = 240 m²

Then the total area of the shaded region is 1320 m².

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1 year ago

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EastWind [94]

Answer:

$B.Alternate\ Exterior\ Angles$

Step-by-step explanation:

$As\ the\ exterior\ angles\ lie\ on\ the\ opposite\ sides\ of\ the\ transversal,\\that\ cuts\ two\ parallel\ lines,\ the\ set\ of\ 'Alternate\ Exterior\ Angles'\ formed\\are\ equal.$