points Q and R are midpoints of the sides of triangle ABC. Triangle A B C is cut by line segment Q R. Point Q is the midpoint of
side A B and point R is the midpoint of side A C. The lengths of A Q and Q B are 4 p, the length of Q R is 2 p + 3, and the length of C B is 6 p minus 4. The lengths of A R and R C are congruent. What is AQ? 10 units 14 units 20 units 32 units
2 answers:
Answer:
AQ = 20 units
Step-by-step explanation:
I tried figuring in the pic below..
Similar triangles are triangles whose corresponding measures are proportional. All of their corresponding angles are also congruent. There are theorems and postulates that prove triangle similarity. Usually they requrie at least three parts of each triangle. The symbol for similarity is ~.
We have two triangles in the figure. ΔAQR and ΔABC. We will prove first that they are similar.
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Answer:
The inequality is
Step-by-step explanation:
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we know that
Solve for x
Subtract 4,885.78 both sides
Divide by 6 both sides
Answer:
The perimeter of the kite JKLM is 50 units ⇒ C
Step-by-step explanation:
The longest diagonal of the kite is its axis of symmetry which means the longest diagonal divides the kite into two congruent triangles
∵ JKLM is a kite
∵ KM is the longest diagonal
∴ KM is divides the kite into two congruent triangles
∴ Δ JKM is congruent to Δ LKM
∴ JK = LK
∴ JM = ML
∵ ML = 10 units
∴ JM = 10 units
∵ The diagonals of the kite are perpendicular
∴ KM ⊥ JL
∵ KM and JL intersected at N
∴ m∠JNK = 90°
∵ KM is the axis of symmetry of kite JKLM
∴ KM bisects JL at N
∴ JN = NL = JL
∵ JL = 18 units
∴ JN = (18)
∴ JN = 9 units
In Δ JNK
∵ m∠JNK = 90°
∵ JN = 9 units
∵ NK = 12 units
- By using Pythagoras Theorem
∵ (JK)² = (JN)² + (NK)²
∴ (JK)² = (9)² + (12)²
∴ (JK)² = 81 + 144
∴ (JK)² = 225
- Take √ for both sides
∴ JK = 15 units
∵ Jk = LK
∴ Lk = 15 units
∵ The perimeter of the kite is the sum of its 4 sides
∴ P = JK + KL + LM + MJ
∵ JK = LK = 15
∵ JM = ML = 10
∴ P = 15 + 15 + 10 + 10
∴ P = 50
The perimeter of the kite JKLM is 50 units