{"id":7576,"date":"2020-09-22T10:30:15","date_gmt":"2020-09-22T05:00:15","guid":{"rendered":"https:\/\/online.2iim.com\/cat-exam\/blogs\/?p=7576"},"modified":"2020-09-22T10:30:16","modified_gmt":"2020-09-22T05:00:16","slug":"cat-quants-interesting-true-false-questions-from-geometry","status":"publish","type":"post","link":"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-quantitative-aptitude\/cat-quants-interesting-true-false-questions-from-geometry\/","title":{"rendered":"CAT Quants | Interesting True\/False Questions from Geometry"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/CAT-Quants-Interesting-True_False-Questions-from-Geometry-1-1024x576.png?resize=768%2C432&#038;ssl=1\" alt=\"CAT Quants | Interesting True\/False Questions from Geometry\" class=\"wp-image-7593\" width=\"768\" height=\"432\" data-recalc-dims=\"1\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-justify\"><em><strong>Geometry<\/strong><\/em> and Arithmetic account for a major chunk of the Quant section for the CAT Exam. Here are a few interesting true\/false questions from Geometry. Happy Solving!<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><em>Check out this wonderful <a href=\"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-preparation-strategy\/cat-geometry-preparation-strategy\/\" target=\"_blank\" rel=\"noreferrer noopener\">article which talks about preparing for Geometry<\/a>!<\/em> <\/h4>\n\n\n\n<h2 class=\"wp-block-heading\">CAT Quants | True\/False Questions from Geometry <\/h2>\n\n\n\n<p class=\"has-text-align-justify\">State whether the following statements are <em><strong>true or false<\/strong><\/em>:<\/p>\n\n\n\n<p><em>1. A parallelogram that circumscribes a circle has to be a square<br>2. A trapezium inscribed in a circle has to be an isosceles trapezium<br>3. Orthocenter of a triangle can lie outside the triangle<br>4. Triangle with sides a, b and c has the relationship a^2&nbsp;+ b^2 &gt; c^2, the triangle has to be acute-angled.<br>5. Diagonals of a parallelogram are angle bisectors of the angles of a parallelogram.<\/em><\/p>\n\n\n\n<p class=\"has-text-align-justify\">Try solving these! For <em><strong>answers and explanations<\/strong><\/em>, scroll down AFTER your attempt! <\/p>\n\n\n\n\n\n<h2 class=\"wp-block-heading\">CAT Quants | Solutions to True\/False Questions from Geometry<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">1. <em>A parallelogram that circumscribes a circle has to be a square<\/em>: <span class=\"has-inline-color has-vivid-red-color\">FALSE<\/span><\/h4>\n\n\n\n<p class=\"has-text-align-justify\">In a parallelogram, opposite sides are equal. In a quadrilateral, the sums of <em>pairs<\/em> of opposite sides are equal. So, a parallelogram that circumscribes a circle should have all 4 of its sides equal. Or, it should be a Rhombus; it need not be a square.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2. <em>A trapezium inscribed in a circle has to be an isosceles trapezium<\/em>: <span class=\"has-inline-color has-vivid-green-cyan-color\">TRUE<\/span><\/h4>\n\n\n\n<p class=\"has-text-align-justify\">An isosceles trapezium is a symmetric diagram. The two base angles should be equal and the two top angles should be equal. So, a trapezeium where the base angles were equal would be an isosceles trapezium.<\/p>\n\n\n\n<p class=\"has-text-align-justify\">In any cyclic quadrilateral, opposite angles would be supplementary. In a trapezium, co-interior angles between the parallel lines would be supplementary. <\/p>\n\n\n\n<p class=\"has-text-align-justify\">So, if we took a trapezium ABCD with AB parallel to CD inscribed in a circle. Angle A and Angle D would be supplementary (co-interior angles). And Angle A and Angle C would be supplementary (opposite angles of a cyclic quadrilateral). Or angle B would be equal to angle C. Ergo, isosceles trapezium.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/batman-thinking-6.gif?resize=329%2C226&#038;ssl=1\" alt=\"batman thinking \" class=\"wp-image-7587\" width=\"329\" height=\"226\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">3. <em>Orthocenter of a triangle can lie outside the triangle<\/em>: <span class=\"has-inline-color has-vivid-green-cyan-color\">TRUE<\/span><\/h4>\n\n\n\n<p class=\"has-text-align-justify\">For any obtuse-angled triangle, two of the altitudes would lie outside the triangle, and would intersect at a point outside the triangle. So, the orthocenter can lie outside the triangle.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4. <em>Triangle with sides a, b and c has the relationship a^2&nbsp;+ b^2 &gt; c^2, the triangle has to be acute-angled<\/em>: <span class=\"has-inline-color has-vivid-red-color\">FALSE<\/span><\/h4>\n\n\n\n<p class=\"has-text-align-justify\">Let us take triangle with sides 2, 3 and 4. 4^2&nbsp;+ 3^2 &gt; 2^2. But &nbsp;as 2^2&nbsp;+ 3^3 &lt; 4^2, the triangle is obtuse-angled. Is a^2&nbsp;+ b^2 &gt; c^2, we can say angle C is acute-angled. We cannot say all three angles are acute-angled. One can use cosine rule also for having a go at this question (though it should be considered inelegant)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">5. <em>Diagonals of a parallelogram are angle bisectors of the angles of a parallelogram<\/em>: <span class=\"has-inline-color has-vivid-red-color\">FALSE<\/span><\/h4>\n\n\n\n<p class=\"has-text-align-justify\">Diagonals of a parallelogram bisect each other. They need not bisect the angles of the parallelogram. Imagine this, if we took a rectangle and studied its diagonals. if the diagonals bisected each other, the angle between diagonal and a side would be 45 degrees. Or, we would end up having a square. <\/p>\n\n\n\n<p class=\"has-text-align-justify\">So, any rectangle that was not a square would have diagonals that were not angle bisectors. So, diagonals of a parallelogram NEED NOT be angle bisectors of the angles of a parallelogram.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">A Final Note:<\/h2>\n\n\n\n<p class=\"has-text-align-justify\">The CAT 2020 Pattern has changed, leaving many aspirants confused and worried about the number of questions. You might want to check out <a href=\"https:\/\/online.2iim.com\/cat-exam\/blogs\/cat-preparation-strategy\/cat-2020-pattern-change-how-to-prepare-for-the-new-pattern\/\" target=\"_blank\" rel=\"noreferrer noopener\">this article about preparing for these changes in the CAT 2020 exam pattern<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/i0.wp.com\/online.2iim.com\/cat-exam\/blogs\/wp-content\/uploads\/2020\/09\/OrangeOrderlyGrouse-max-1mb.gif?resize=240%2C240&#038;ssl=1\" alt=\"math dance - geometry\" class=\"wp-image-6798\" width=\"240\" height=\"240\" data-recalc-dims=\"1\" \/><\/figure><\/div>\n\n\n\n<p><a href=\"https:\/\/www.who.int\/emergencies\/diseases\/novel-coronavirus-2019\/advice-for-public\" target=\"_blank\" rel=\"noreferrer noopener\">Stay Safe<\/a>, Best Wishes for CAT!<\/p>\n\n\n\n<p><a rel=\"noreferrer noopener\" href=\"https:\/\/www.quora.com\/profile\/Rajesh-Balasubramanian-8\" target=\"_blank\"><em>Rajesh Balasubramanian<\/em><\/a><em> takes the CAT every year and is a 4-time CAT 100 percentiler.&nbsp;He likes few things more than teaching Math and insists to this day that he is a better teacher than exam-taker.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Geometry and Arithmetic account for a major chunk of the Quant section for the CAT Exam. Here are a few interesting true\/false questions from Geometry. Happy Solving!<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[2],"tags":[284,286,474],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>CAT Quants | Interesting True\/False Questions from Geometry - 2IIM<\/title>\n<meta name=\"description\" content=\"Geometry and Arithmetic account for a huge chunk of CAT Quants. Here are a few interesting true\/false questions from Geometry. 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