Chapter 4: Q5. (page 132)

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Short Answer

Expert verified

$Δ T R P ≅ Δ T R S$ by ASA (Angle-Side-Angle) Postulate

Step by step solution

Step 1. First observation from figure.

Line segment $\bar{T R}$ is common in both triangles.

So, by reflexive property of congruency

$\bar{T R} ≅ \bar{T R}$

Step 2. Find ∠TRP.

Since sum of angles of a triangle is $180 °$

$\begin{matrix} ∠ T R P + ∠ R P T + ∠ P T R = 180 ° \\ ∠ T R P + 60 ° + 50 ° = 180 ° \\ ∠ T R P = 180 ° - 110 ° \\ ∠ T R P = 70 ° \end{matrix}$

Step 3. Find ∠RTS.

Since sum of angles of a triangle is $180 °$

$∠ R T S + ∠ T S R + ∠ S R T = 180 ° ∠ R T S + 60 ° + 70 ° = 180 ° ∠ R T S = 180 ° - 130 ° ∠ R T S = 50 °$

Step 4. Observations from figure and above steps.

$∠ T R P$ and $∠ T R S$ are congruent

So, $∠ T R P ≅ ∠ T R S$

Also, $∠ P T R$ and $∠ S T R$ are congruent

So, $∠ P T R ≅ ∠ S T R$

Step 5. Conclude given two triangles are congruent or not.

From step 1 and 4

Two angles and there including side is congruent

Thus, $Δ T R P ≅ Δ T R S$ by ASA (Angle-Side-Angle) Postulate

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Short Answer

Step by step solution

Step 1. First observation from figure.

Step 2. Find ∠TRP.

Step 3. Find ∠RTS.

Step 4. Observations from figure and above steps.

Step 5. Conclude given two triangles are congruent or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Geometry

Calculus

Statistics

Study anywhere. Anytime. Across all devices.