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Aleks [24]
1 year ago
5

Name the property that justifies each statement.If ∠DEF≅∠HJK, then ∠HJK≅∠DEF..

Mathematics
1 answer:
o-na [289]1 year ago
6 0

The property that justifies this statement is the Symmetric Property of Congruence.

<h3>What is symmetric property of Congruence?</h3>

The symmetric property of congruence states that If an angle is congruent to another angle, then the second angle is also congruent to the first angle.

A congruent geometric shapes are shapes having the same size and shape, or matching in size and shape and their corresponding angles are equal to each other.

If shape A is congruent to shape B and A= B , then B = A

Similarly,

If angle DEF is equal to angle HJK, then with the law of symmetry property of angle HJk is equal to angle DEF.

learn more about symmetric property of

Congruence from

brainly.com/question/8762236

#SPJ1

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Answer:

Proved See below

Step-by-step explanation:

Man this one is a world of its own :D Just a quick question are you a fellow Add Math student in O levels i remember this question from back in the day :D Anyhow Lets get started

For this question we need to know the following identities:

1+tan^{2}x=sec^2x\\\\1+cot^2x=cosec^2x\\\\sin^2x+cos^2x=1

Lets solve the bottom most part first:

1-\frac{1}{1-sec^2x} \\\\

Take LCM

1-\frac{1}{1-sec^2x} \\\\\frac{1-sec^2x-1}{1-sec^2x} \\\\\frac{-sec^2x}{1-sec^2x} \\\\\frac{-(1+tan^2x)}{-tan^2x}

now break the LCM

\frac{-1}{-tan^2x}+\frac{-tan^2x}{-tan^2x}\\\\\frac{1}{tan^2x}+1\\\\cot^2x+1

because 1/tan = cot x

and furthermore,

cot^2x+1\\cosec^2x

now we solve the above part and replace the bottom most part that we solved with cosec^2x

\frac{1}{1-\frac{1}{cosec^2x} } \\\\\frac{1}{1-sin^2x} \\\\\frac{1}{cos^2x}\\\\sec^2x

Hence proved! :D

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I hope helped ^^

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