How do i write a two column proof for this??Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST

Mathematics

1 answer:

Nikolay [14]4 years ago

7 0

Answer:

PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)

Step-by-step explanation:

Given: PG ≅ SG and PT ≅ ST

To Prove: ∠GPT ≅ ∠GST

Proof: PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).

SSS Congruency Axiom: If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

Congruence: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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At 10:00 a.M., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs

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Answer: 1. Han run 2.5 miles after a half hour.

2. No, they will not meet within 1 hour.

Step-by-step explanation:

Here, Han runs at a pace of 12 minutes per mile.

Or, we can say that he can run with the speed of 5 miles per hour. (because, speed = 1/pace and 12 minutes = 1 miles ⇒ 60 minutes = 5 miles)

Similarly, If Tyler runs at a pace of 15 minutes per mile ⇒ Tyler run with the speed of 4 miles per hour.

Therefore,

1) The distance covered by Han in half an hour = 1/2 × 5 = 2.5 miles

(because distance = speed × time)