NEED HELP ASAP PLEASE!! The provided diagram of triangle ABC will help you to prove that the base angles of an isosceles triangl
e are congruent. The first step is to draw auxiliary line AO. What must be true about in order to complete the proof using the ASA (Angle Side Angle) triangle congruency theorem? Classify each statement as needed or not needed to complete the proof.
1 answer:
Answer: The proof is mentioned below.
Step-by-step explanation:
Here, Δ ABC is isosceles triangle.
Therefore, AB = BC
Prove: Δ ABO ≅ Δ ACO
In Δ ABO and Δ ACO,
∠ BAO ≅ ∠ CAO ( AO bisects ∠ BAC )
∠ AOB ≅ ∠ AOC ( AO is perpendicular to BC )
BO ≅ OC ( O is the mid point of BC)
Thus, By ASA postulate of congruence,
Δ ABO ≅ Δ ACO
Therefore, By CPCTC,
∠B ≅ ∠ C
Where ∠ B and ∠ C are the base angles of Δ ABC.
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Answer:
The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.
Step-by-step explanation:
Let <em>x</em> be one leg of the right triangle.
Since the other leg is two centimeters longer, it can be represented by the expression:
According to the Pythagorean Theorem, for a right triangle:
Where <em>c</em> is the hypotenuse and <em>a</em> and <em>b</em> are the two legs.
The hypotenuse is given to be 6 cm and the two legs are <em>x</em> and (<em>x</em> + 2). Hence:
Solve for <em>x</em>. Simplify:
Simplify:
Subtract:
Divide:
The equation is not factorable, so we can consider using the quadratic formula:
In this case, <em>a</em> = 1, <em>b</em> = 2, and <em>c</em> = -16. Substitute:
And evaluate:
Hence, our two solutions are:
Lengths cannot be negative, so we can ignore the second solution.
Hence, the value of <em>x</em> or the first side length is about 3.1 centimeters.
Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.
In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.